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Homework answers / question archive / 1) Assume that you have paired values consisting of heights (in inches) and weights (in Ib) from 40 randomly selected men
1) Assume that you have paired values consisting of heights (in inches) and weights (in Ib) from 40 randomly selected men. The linear correlation coefficient r is 0.537. Find the value of the coefficient of determination. What practical information does the coefficient of determination provide?
Choose the correct answer below.
A. The coefficient of determination is 0.712. 28.8% of the variation is explained by the linear correlation, and 71.2% is explained by other factors.
B. The coefficient of determination is 0.712. 71.2% of the variation is explained by the linear correlation, and 28.8% is explained by other factors.
C. The coefficient of determination is 0.288. 28.8% of the variation is explained by the linear correlation, and 71.2% is explained by other factors.
D. The coefficient of determination is 0.288. 71.2% of the variation is explained by the linear correlation, and 28.8% is explained by other factors.
2) Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables.
r= 0.588
What is the value of the coefficient of determination?
r2 = (Round to four decimal places as needed.)
What is the percentage of the total variation that can be explained by the linear relationship between the two variables?
Explained variation = ___________________% (Round to two decimal places as needed.)
3. Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables.
r= - 0.453
What is the value of the coefficient of determination?
r2 = (Round to four decimal places as needed.)
What is the percentage of the total variation that can be explained by the linear relationship between the two variables?
Explained variation = ______________________ % (Round to two decimal places as needed.)
4. The Minitab output shown below was obtained by using paired data consisting of weights (in Ib) of 32 cars and their highway fuel consumption amounts (in mi/gal). Along with the paired sample data, Minitab was also given a car weight of 5000 Ib to be used for predicting the highway fuel consumption amount. Use the information provided in the display to determine the value of the linear correlation coefficient. (Be careful to correctly identify the sign of the correlation coefficient.) Given that there are 32 pairs of data, is there sufficient evidence to support a claim of linear correlation between the weights of cars and their highway fuel consumption amounts?
1Click the icon to view the Minitab display.
The linear correlation coefficient is __________.
(Round to three decimal places as needed.)
Is there sufficient evidence to support a claim of linear correlation?
1: Minitab output
The regression equation is
Highway = 50.8 — 0.00580 Weight
|
Predictor |
Coef |
SE Coef |
T |
P |
|
Constant |
50.801 |
2.844 |
17.46 |
0.000 |
|
Weight |
-0.0057967 |
0.0007555 |
-7.54 |
0.000 |
S = 2.29741 R – Sq = 63.8% R – Sq(adj) = 61.3%
Predictor Value for New Observations
New
Obs Fit SE Fit 95% CI 95%PI
1 21.818 0.525 (20.803, 22.833) (17.227, 26.409)
Values of Predictors for New Observations
New
Obs Weight
1 5000
Section 10.4 Homework [rrr
5. The accompanying technology output was obtained by using the paired data consisting of foot lengths (cm) and heights (cm) of a sample of 40 people. Along with the paired sample data, the technology was also given a foot length of 13.2 cm to be used for predicting height. The technology found that there is a linear correlation between height and foot length. If someone has a foot length of 13.2 cm, what is the single value that is the best predicted height for that person?
2 Click the icon to view the technology output.
The single value that is the best predicted height is_____________ cm.
(Round to the nearest whole number as needed. )
2: Technology Output
The regression equation is
Height = 54.7 + 4.15 Foot Length
Predictor Coef SE Coef T P
Constant 54.67 11.02 4.96 0.000
Foot Length 4.1547 0.4626 8.98 0.000
S = 5.50642 R-Sq = 70.6% R-Sq(adj) = 69.8%
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 109.512 1.783 (104.853, 114.171) (98.497, 120.527)
Values of Predictors for New Observations
Foot
New Obs Length
1 13.2
6. Over the years, it was noticed that the cost of a slice of pizza and the cost of a subway fare in a certain city seemed to increase by the same amounts. Let x represent the cost of a slice of pizza and let y represent the corresponding subway fare. Use the following statistics that were obtained from a random sample of costs (in dollars) of pizza/subway fares to construct a prediction interval estimate of the subway fare with 99% confidence when the cost of a slice of pizza is $2.90.
n = 6 b0 = 0.03456 b1 = 0.94502
X = 1.0833333 Sx = 6.50 Sx2 = 9.77 Se = 0.123
The 99% prediction interval is ____________ <y< __________.
(Round to two decimal places as needed.)
Section 10.4 Homework-n 6/16/21, 1:53 PM
7. Over the years, it was noticed that the cost of a slice of pizza and the cost of a subway fare in a certain city seemed to increase by the same amounts. Let x represent the cost of a slice of pizza and let y represent the corresponding subway fare. Use the following statistics that were obtained from a random sample of costs (in dollars) of pizza/subway fares to construct a prediction interval estimate of the subway fare with 95% confidence when the cost of a slice of pizza is $1.20.
n=6 b0 = 0.03456 b1 = 0.94502
X= 1.0833333 Sx = 6.50 Sx2 = 9.77 Se = 0.123
The 95% prediction interval is_________ <y< _________.
(Round to two decimal places as needed.)
8. Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet).
Altitude 2 9 16 24 29 31 34
Temperature 60 31 22 -4 - 29 -41 - 51
a. Find the explained variation.
(Round to two decimal places as needed.)
b. Find the unexplained variation.
(Round to five decimal places as needed.)
c. Find the indicated prediction interval.
_______________°F<y< ____________ °F
(Round to four decimal places as needed.)
9. Listed below are amounts of court income and salaries paid to the town justices for a certain town. All amounts are in thousands of dollars. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 99% confidence level with a court income of $800,000.
Court Income $70 $401 $1587 $1149 $292 $252 $113 $158 $27
Justice Salary $27 $45 $99 $52 $40 $56 $25 $29 $23
a. Find the explained variation.
(Round to three decimal places as needed. )
b. Find the unexplained variation.
(Round to three decimal places as needed. )
c. Find the indicated prediction interval.
$_______ <y<$_______
(Round to four decimal places as needed. )
10. The table below lists measured amounts of redshift and the distances (billions of light-years) to randomly selected astronomical objects. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 90% confidence level with a redshift of 0.0126.
Redshift 0.0236 0.0535 0.0717 0.0398 0.0441 0.0105
Distance 0.31 0.74 0.99 0.57 0.62 0.15
a. Find the explained variation.
(Round to six decimal places as needed.)
b. Find the unexplained variation.
(Round to six decimal places as needed.)
c. Find the indicated prediction interval.
________________billion light-years < y < __________billion light-years
(Round to three decimal places as needed. )
Section 10.4 Homework-n 6/16/21, 1:53 PM
11. The table below lists weights (carats) and prices (dollars) of randomly selected diamonds. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with a diamond that weighs 0.8 carats.
Weight 0.3 0.4 0.5 0.5 1.0 0.7
Price $514 $1159 $1335 $1421 $5664 $2277
a. Find the explained variation.
(Round to the nearest whole number as needed. )
b. Find the unexplained variation.
(Round to the nearest whole number as needed. )
c. Find the indicated prediction interval.
$_______ <y<$________
(Round to the nearest whole number as needed. )
12. Fill in the blank.
The ____________ deviation of (x,y) is the vertical distance y- y, which is the distance between the point (x,y) and the horizontal line passing through the sample mean y.
The (1)___s deviation of (x,y) is the vertical distance y - y, which is the distance between the point (x,y) and the horizontal line passing through the sample mean y.
(1) explained
partial
total
unexplained
13. Fill in the blank.
The coefficient of determination, r2 is the amount of variation in______ that is explained by the regression line.
The coefficient of determination, r2, is the amount of variation in (1) ____________ that is explained by the regression line.
(1) r
X
s
Y
14. Fill in the blank.
A______ is an interval estimate of a predicted value of y.
A (1) _________ is an interval estimate of a predicted value of y.
(1) confidence interval
prediction interval
residual
standard error of estimate
15. Fill in the blank.
The ______ is a measure of the differences between the observed sample y-values and the predicted values y that are obtained using the regression equation.
The (1) ______ is a measure of the differences between the observed sample y-values and the predicted values y that are obtained using the regression equation.
(1) confidence interval
prediction interval
standard error of estimate
residual
16. Fill in the blank.
The______ deviation is the vertical distance y — y, which is the distance between the predicted y-value and the horizontal line passing through the sample mean y.
The (1)______ deviation is the vertical distance y - y, which is the distance between the predicted y-value and the horizontal line passing through the sample mean y.
(1) unexplained
explained
standard
total
1) The table below lists days of the week selected by a random sample of 1000 subjects who were asked to identify the day of the week that is best for quality family time. Consider the claim that the days of the week are selected with a uniform distribution so that all days have the same chance of being selected. If we test the claim using the goodness-of-fit test, what is actually tested?
Sun Mon Tues Wed Thurs Fri Sat
523 15 10 19 12 42 379
Choose the correct answer below.
A. The test is to determine whether the observed frequency counts agree with the claimed uniform distribution so that the frequencies for only two days are equally likely.
B. The test is to determine whether the observed frequency counts agree with the claimed uniform distribution so that the frequencies for the different days are equally likely.
C. The test is to determine whether the observed frequency counts agree with the claimed uniform distribution so that the frequencies for at least two days are equally likely.
D. The test is to determine whether the observed frequency counts agree with the claimed chi-square distribution so that the frequencies for at most three days are equally likely.
2) A random sample of 791 subjects was asked to identify the day of the week that is best for quality family time. Consider the claim that the days of the week are selected with a uniform distribution so that all days have the same chance of being selected. The table below shows goodness-of-fit test results from the claim and data from the study. Test that claim using either the critical value method or the P-value method with an assumed significance level of α = 0.05.
Test statistic,
Num Categories 7 c2 3873.428
Degrees of freedom 6 Critical c2 12.592
Expected Freq 113.0000 P-Value 0.0000
Determine the null and alternative hypotheses.
H0: (1)________
H1: (2)________
Identify the test statistic.
c2 =______ (Type an integer or a decimal.)
Identify the critical value.
c2 =______ (Type an integer or a decimal.)
State the conclusion.
(3) ______ H0. There (4)_____ sufficient evidence to warrant rejection of the claim that the days of the week are selected with a uniform distribution. It (5) ______ that all days have the same chance of being selected.
(1) At least two days of week have a different frequency of being selected.
All days of the week have an equal chance of being selected.
At least one day of the week has a different chance of being selected.
All days of the week have a different chance of being selected.
(2) All days of the week have a different chance of being selected.
All days of the week have an equal chance of being selected.
At least two days of the week have a different frequency of being selected.
At least one day of the week has a different chance of being selected.
(3) Reject
Fail to reject
(4) is not
Is
(5) does not appear
Does appear
3. Conduct the hypothesis test and provide the test statistic, critical value and P-value, and state the conclusion.
A person purchased a slot machine and tested it by playing it 1,208 times. There are 10 different categories of outcomes, including no win, win jackpot, win with three bells, and so on. When testing the claim that the observed outcomes agree with the expected frequencies, the author obtained a test statistic of χ2 = 15.707. Use a 0.10 significance level to test the claim that the actual outcomes agree with the expected frequencies. Does the slot machine appear to be functioning as expected?
The test statistic is______. (Type an integer or a decimal.)
The critical value is _____. (Round to three decimal places as needed.)
The P-value is______. (Round to four decimal places as needed.)
State the conclusion.
(1) _____H0. There (2) ___ sufficient evidence to warrant rejection of the claim that the observed outcomes agree with the expected frequencies. The slot machine (3) ________to be functioning as expected.
1: Chi-square distribution table
|
Area to the Right of the Critical Value |
|||||||||
|
Degrees of Freedom |
0.995 |
0.99 |
0.975 |
0.95 |
0.90 |
0.10 |
0.05 |
0.025 |
0.01 |
|
1 |
- |
- |
0.001 |
0.004 |
0.016 |
2.706 |
3.841 |
5.024 |
6.635 |
|
2 |
0.010 |
0.020 |
0.051 |
0.103 |
0.211 |
4.605 |
5.991 |
7.378 |
9.210 |
|
3 |
0.072 |
0.115 |
0.216 |
0.352 |
0.584 |
6.251 |
7.815 |
9.348 |
11.345 |
|
4 |
0.207 |
0.297 |
0.484 |
0.711 |
1.064 |
7.779 |
9.488 |
11.143 |
13.277 |
|
5 |
0.412 |
0.554 |
0.831 |
1.145 |
1.610 |
9.236 |
11.071 |
12.833 |
15.086 |
|
6 |
0.676 |
0.872 |
1.237 |
1.635 |
2.204 |
10.645 |
12.592 |
14.449 |
16.812 |
|
7 |
0.989 |
1.239 |
1.690 |
2.167 |
2.833 |
12.017 |
14.067 |
16.013 |
18.475 |
|
8 |
1.344 |
1.646 |
2.180 |
2.733 |
3.490 |
13.362 |
15.507 |
17.535 |
20.090 |
|
9 |
1.735 |
2.088 |
2.700 |
3.325 |
4.168 |
14.684 |
16.919 |
19.023 |
21.666 |
|
10 |
2.156 |
2.558 |
3.247 |
3.940 |
4.865 |
15.987 |
18.307 |
20.483 |
23.209 |
(1) Reject
Do not reject
(2) is not
is
(3) does not appear
appears
4) Conduct the hypothesis test and provide the test statistic, critical value and P-value, and state the conclusion.
A person randomly selected 100 checks and recorded the cents portions of those checks. The table below lists those cents portions categorized according to the indicated values. Use a 0.05 significance level to test the claim that the four categories are equally likely. The person expected that many checks for whole dollar amounts would result in a disproportionately high frequency for the first category, but do the results support that expectation?
Cents portion of check 0-24 25-49 50-74 75-99
Number 64 10 13 13
Click here to view the chi-square distribution table.
The test statistic is _______(Type an integer or a decimal.)
The critical value is_________(Round to three decimal places as needed.)
The P-value is __________ (Round to four decimal places as needed.)
State the conclusion
(1)_______H0. There (2) ________sufficient evidence to warrant rejection of the claim that the four categories are equally likely. The results (3) _______to support the expectation that the frequency for the first category is disproportionately high.
2: Chi-square distribution table
|
Area to the Right of the Critical Value |
|||||||||
|
Degrees of Freedom |
0.995 |
0.99 |
0.975 |
0.95 |
0.90 |
0.10 |
0.05 |
0.025 |
0.01 |
|
1 |
- |
- |
0.001 |
0.004 |
0.016 |
2.706 |
3.841 |
5.024 |
6.635 |
|
2 |
0.010 |
0.020 |
0.051 |
0.103 |
0.211 |
4.605 |
5.991 |
7.378 |
9.210 |
|
3 |
0.072 |
0.115 |
0.216 |
0.352 |
0.584 |
6.251 |
7.815 |
9.348 |
11.345 |
|
4 |
0.207 |
0.297 |
0.484 |
0.711 |
1.064 |
7.779 |
9.488 |
11.143 |
13.277 |
|
5 |
0.412 |
0.554 |
0.831 |
1.145 |
1.610 |
9.236 |
11.071 |
12.833 |
15.086 |
|
6 |
0.676 |
0.872 |
1.237 |
1.635 |
2.204 |
10.645 |
12.592 |
14.449 |
16.812 |
|
7 |
0.989 |
1.239 |
1.690 |
2.167 |
2.833 |
12.017 |
14.067 |
16.013 |
18.475 |
|
8 |
1.344 |
1.646 |
2.180 |
2.733 |
3.490 |
13.362 |
15.507 |
17.535 |
20.090 |
|
9 |
1.735 |
2.088 |
2.700 |
3.325 |
4.168 |
14.684 |
16.919 |
19.023 |
21.666 |
|
10 |
2.156 |
2.558 |
3.247 |
3.940 |
4.865 |
15.987 |
18.307 |
20.483 |
23.209 |
(1) Reject
Do not reject
(2) is not
is
(3) do not appear
appear
5) For a recent year, the following are the numbers of homicides that occurred each month in a city. Use a 0.05 significance level to test the claim that homicides in a city are equally likely for each of the 12 months. Is there sufficient evidence to support the police commissioner's claim that homicides occur more often in the summer when the weather is better?
Full data set
Month Number Month Number
Jan. 38 July 46
Feb. 29 Aug. 49
March 45 Sep. 49
April 41 Oct. 43
May 45 Nov. 38
June 48 Dec 38
Determine the null and alternative hypotheses.
H0: (1)___________
H1: (2) __________
Calculate the test statistic, χ2.
Χ2 =________(Round to three decimal places as needed.)
Calculate the P-value.
P-value =_______(Round to four decimal places as needed.)
What is the conclusion for this hypothesis test?
A. Reject H0. There is insufficient evidence to warrant rejection of the claim that homicides in a city are equally likely for each of the 12 months.
B. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that homicides in a city are equally likely for each of the 12 months.
C. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that homicides in a city are equally likely for each of the 12 months.
D. Reject H0. There is sufficient evidence to warrant rejection of the claim that homicides in a city are equally likely for each of the 12 months.
Is there sufficient evidence to support the police commissioner's claim that homicides occur more often in the summer when the weather is better?
A. There is not sufficient evidence to support the police commissioner's claim that homicides occur more often in the summer when the weather is better.
B. There is sufficient evidence to support the police commissioner's claim that homicides occur more often in the summer when the weather is better.
(1) Homicides occur with all different frequencies in the different months.
At least two months have a different frequency of homicides than the others.
At least one month has a different frequency of homicides than the others.
Homicides occur with equal frequency in the different months.
(2) At least one month has a different frequency of homicides than the others.
Homicides occur with all different frequencies in the different months.
Homicides occur with equal frequency in the different months.
At least two months have a different frequency of homicides than the others.
6. Randomly selected birth records were obtained, and categorized as listed in the table to the right. Use a 0.01 significance level to test the reasonable claim that births occur with equal frequency on the different days of the week. How might the apparent lower frequencies on Saturday and Sunday be explained?
Day Sun Mon Tues Wed Thurs Fri Sat
Number of Births 49 55 61 56 59 62 49
Determine the null and alternative hypotheses.
H0 : (1) __________
H1 : (2) ________
Calculate the test statistic, χ2.
χ2 = ________( Round to three decimal places as needed.)
Calculate the P-value.
P-value = _______ ( Round to four decimal places as needed.)
What is the conclusion for this hypothesis test?
A. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week.
B. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week.
C. Reject H0. There is sufficient evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week.
D. Reject H0. There is insufficient evidence to warrant rejection of the claim that births occur with equal frequency on the different days of the week.
How might the apparent lower frequencies on Saturday and Sunday be explained?
A. Induced or Caesarean-section births are scheduled on weekends whenever possible.
B. Induced or Caesarean-section births are scheduled during the week whenever possible.
(1) At least one day has a different frequency of births than the other days. Births occur with the same frequency on the different days of the week.
At least two days have a different frequency of births than the other days.
Births occur with all different frequencies on the different days of the week.
(2) Births occur with the same frequency on the different days of the week.
Births occur with all different frequencies on the different days of the week.
At least one day has a different frequency of births than the other days.
At least two days have a different frequency of births than the other days.
7. The table below lists the frequency of wins for different post positions in a horse race. A post position of 1 is closest to the inside rail, so that horse has the shortest distance to run. (Because the number of horses varies from year to year, only the first 10 post positions are included.) Use a 0.05 significance level to test the claim that the likelihood of winning is the same for the different post positions. Based on the result, should bettors consider the post position of a horse race?
Post Position 1 2 3 4 5 6 7 8 9 10
Wins 19 13 12 16 14 6 9 11 5 10
Determine the null and alternative hypotheses.
H0: (1) ______
H1: (2) ____
Calculate the test statistic, χ2.
χ2 = ( Round to three decimal places as needed.)
Calculate the P-value.
P-value = ( Round to four decimal places as needed.)
What is the conclusion for this hypothesis test?
A. Reject H0. There is insufficient evidence to warrant rejection of the claim that the likelihood of winning is the same for the different post positions.
B. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the likelihood of winning is the same for the different post positions.
C. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the likelihood of winning is the same for the different post positions..
D. Reject H0. There is sufficient evidence to warrant rejection of the claim that the likelihood of winning is the same for the different post positions.
Based on the result, should bettors consider the post position of a horse race?
No
Yes
(1) At least one post positions have a different frequency of wins than the others.
Wins occur with all different frequency in the different post positions.
Wins occur with equal frequency in the different post positions.
At least one post position has a different frequency of wins than the others.
(2) At least one post position has a different frequency of wins than the others.
Wins occur with all different frequency in the different post positions.
At least one post positions have a different frequency of wins than the others.
Wins occur with equal frequency in the different post positions.
8. The table below lists the number of games played in a yearly best-of-seven baseball championship series, along with the expected proportions for the number of games played with teams of equal abilities. Use a 0.05 significance level to test the claim that the actual numbers of games fit the distribution indicated by the expected proportions.
Games Played 4 5 6 7
Actual contests 20 19 24 36
Expected proportion 2/16 4/16 5/16 5/16
Determine the null and alternative hypotheses.
H0 : (1)
H1 : (2)
Calculate the test statistic, χ2.
χ2 = ( Round to three decimal places as needed.)
Calculate the P-value.
P-value = ( Round to four decimal places as needed.)
What is the conclusion for this hypothesis test?
A. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the actual numbers of games fit the distribution indicated by the expected proportions.
B. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the actual numbers of games fit the distribution indicated by the expected proportions.
C. Reject H0. There is sufficient evidence to warrant rejection of the claim that the actual numbers of games fit the distribution indicated by the expected proportions.
D. Reject H0. There is insufficient evidence to warrant rejection of the claim that the actual numbers of games fit the distribution indicated by the expected proportions..
(1) The observed frequencies agree with the expected proportions.
At least one of the observed frequencies do not agree with the expected proportions.
The observed frequencies agree with three of the expected proportions. The observed frequencies agree with two of the expected proportions.
(2) The observed frequencies agree with the expected proportions.
At least one of the observed frequencies do not agree with the expected proportions.
The observed frequencies agree with two of the expected proportions.
The observed frequencies agree with three of the expected proportions.
9. Conduct the hypothesis test and provide the test statistic, critical value and P-value, and state the conclusion.
A package of 100 candies are distributed with the following color percentages: 12 % red, 22 % orange, 15 % yellow, 11 % brown, 23 % blue, and 17 % green. Use the given sample data to test the claim that the color distribution is as claimed. Use a 0.01 significance level.
3 Click the icon to view the color counts for the candy in the package.
Click here to view the chi-square distribution table.4
( Round to two decimal places as needed.)
The critical value is .
( Round to three decimal places as needed.)
The P-value is .
( Round to three decimal places as needed.) State the conclusion.
(1) ________ H0. There (2)________ sufficient evidence to warrant rejection of the claim that the color distribution is as claimed.
3: Candy Package Counts
Candy Counts
Color Number in Package
Red 11
Orange 25
Yellow 7
Brown 12
Blue 27
Green 18
4: Chi-square distribution table
|
Area to the Right of the Critical Value |
|||||||||
|
Degrees of Freedom |
0.995 |
0.99 |
0.975 |
0.95 |
0.90 |
0.10 |
0.05 |
0.025 |
0.01 |
|
1 |
- |
- |
0.001 |
0.004 |
0.016 |
2.706 |
3.841 |
5.024 |
6.635 |
|
2 |
0.010 |
0.020 |
0.051 |
0.103 |
0.211 |
4.605 |
5.991 |
7.378 |
9.210 |
|
3 |
0.072 |
0.115 |
0.216 |
0.352 |
0.584 |
6.251 |
7.815 |
9.348 |
11.345 |
|
4 |
0.207 |
0.297 |
0.484 |
0.711 |
1.064 |
7.779 |
9.488 |
11.143 |
13.277 |
|
5 |
0.412 |
0.554 |
0.831 |
1.145 |
1.610 |
9.236 |
11.071 |
12.833 |
15.086 |
|
6 |
0.676 |
0.872 |
1.237 |
1.635 |
2.204 |
10.645 |
12.592 |
14.449 |
16.812 |
|
7 |
0.989 |
1.239 |
1.690 |
2.167 |
2.833 |
12.017 |
14.067 |
16.013 |
18.475 |
|
8 |
1.344 |
1.646 |
2.180 |
2.733 |
3.490 |
13.362 |
15.507 |
17.535 |
20.090 |
|
9 |
1.735 |
2.088 |
2.700 |
3.325 |
4.168 |
14.684 |
16.919 |
19.023 |
21.666 |
|
10 |
2.156 |
2.558 |
3.247 |
3.940 |
4.865 |
15.987 |
18.307 |
20.483 |
23.209 |
(1) Do not reject
Reject
(2) is not
is
10. Fill in the blank.
A _____________ is used to test the hypothesis that an observed frequency distribution fits (or conforms to) some claimed distribution.
A (1)_________ is used to test the hypothesis that an observed frequency distribution fits (or conforms to) some claimed distribution.
(1) F test
One-way analysis of variance
Student t-test
Goodness –of –fit test
11. Which of the following is NOT a requirement to conduct a goodness-of-fit test?
Choose the correct answer below.
A. For each category, the observed frequency is at least 5.
B. The data have been randomly selected.
C. The sample data consist of frequency counts for each of the different categories.
D. For each category, the expected frequency is at least 5.
12. Which of the following is NOT true of the goodness-of-fit test?
Choose the correct answer below.
A. Expected frequencies need not be whole numbers.
B. Goodness-of-fit hypothesis tests may be left-tailed, right-tailed, or two-tailed.
C. If expected frequencies are equal, then we can determine them by E = n/k, where n is the total number of observations and k is the number of categories
D. If expected frequencies are not all equal, then we can determine them by E = np for each individual category, where n is the total number of observations and p is the probability for the category.
13. Which of the following is NOT true of the χ2 test statistic?
Choose the correct answer below.
A. The χ2 test statistic is based on differences between the observed and expected values.
B. A small χ2 test statistic leads us to conclude that there is not a good fit with the assumed distribution.
C. If the observed and expected frequencies are not close, the χ2 test statistic will be large and the P-value will be small.
1) The accompanying table summarizes successes and failures when subjects used different methods when trying to stop smoking. The determination of smoking or not smoking was made five months after the treatment was begun. If we test the claim that success is independent of the method used, the technology provides a P-value of 0.037 (rounded). What does the P-value tell us about that claim?
Click the icon to view the stop smoking data.
What does the P-value tell us about that claim?
Because the P-value of 0.037 (1) _______ small (such as 0.05 or lower), (2) ________the null hypothesis of independence between the treatment and whether the subject stops smoking. This suggests that the choice of treatment (3)________.
1: Stop Smoking Data
|
|
Nicotine Gum |
Nicotine Patch |
Nicotine Inhaler |
|
Smoking |
192 |
274 |
91 |
|
Not Smoking |
58 |
65 |
39 |
(1) is
Is not
(2) reject
Fail to reject
(3) Appears to make a difference.
Does not appear to make much of a difference.
2) Winning team data were collected for teams in different sports, with the results given in the table below. Use the TI-83/84 Plus results at a 0.05 level of significance to test the claim that home/visitor wins are independent of the sport.
TI-83/84 PLUS
c2 – Test
c2 = 9.881211037
P = 0.0196033482
df = 3
|
|
Basketball |
Baseball |
Hockey |
Football |
|
Home team wins |
135 |
57 |
51 |
69 |
|
Visiting team wins |
63 |
49 |
44 |
35 |
(1) ________________the null hypothesis that home/visitor wins are independent of the sport. It appears that the home-field advantage (2)_____________ depend on the sport.
(1) Fail to reject
Reject
(2) does not
Does
3. The table below summarizes results for randomly selected drivers stopped by police in a recent year. Using technology, the data in the table results in the statistics that follow.
Black and Non-Hispanic White and Non-Hispanic
Stopped by police 18 208
Not stopped by police 178 1017
Chi-square statistic = 7.678, degrees of freedom = 1, P-value = 0.006
Use a 0.05 significance level to test the claim that being stopped is independent of race. Based on available evidence, can we conclude that racial profiling is being used?
Can we conclude that racial profiling is being used?
A. Yes, because the P-value is less than the significance level.
B. No, because the P-value is less than the significance level.
C. Yes, because the P-value is greater than the significance level.
D. No, because the P-value is greater than the significance level.
4. The table below includes results from polygraph (lie detector) experiments conducted by researchers. In each case, it was known if the subjected lied or did not lie, so the table indicates when the polygraph test was correct. Use a 0.05 significance level to test the claim that whether a subject lies is independent of the polygraph test indication. Do the results suggest that polygraphs are effective in distinguishing between truth and lies?
Click the icon to view the table.
Determine the null and alternative hypotheses.
A. H0: Whether a subject lies is independent of the polygraph test indication.
H1: Whether a subject lies is not independent of the polygraph test indication.
B. H0: Whether a subject lies is not independent of the polygraph test indication.
H1: Whether a subject lies is independent of the polygraph test indication.
C. H0: Polygraph testing is not accurate.
H1: Polygraph testing is accurate.
D. H0: Polygraph testing is accurate.
H1: Polygraph testing is not accurate.
Determine the test statistic.
Χ2= _____________ (Round to three decimal places as needed.)
Determine the P-value of the test statistic.
P-value = ___________ (Round to four decimal places as needed.)
Do the results suggest that polygraphs are effective in distinguishing between truth and lies?
A. There in not sufficient evidence to warrant rejection of the claim that polygraph testing is 95% accurate.
B. There is not sufficient evidence to warrant rejection of the claim that polygraph testing is 95% accurate.
C. There is not sufficient evidence to warrant rejection of the claim that whether a subject lies is independent of the polygraph test indication.
D. There is not sufficient evidence to warrant rejection of the claim that whether a subject lies is independent of the polygraph test indication.
2: More info
|
|
Did the Subject Actually Lie? |
|
|
No (Did Not Lie) |
Yes (Lied) |
|
|
Polygraph test indicated that the subject lied. |
9 |
50 |
|
Polygraph test indicated that the subject did not lie. |
35 |
7 |
5) Results from a civil servant exam are shown in the table to the right. Is there sufficient evidence to support the claim that the results from the test are discriminatory? Use a 0.01 significance level.
|
|
Passed |
Failed |
|
White candidates |
16 |
13 |
|
Minority candidates |
11 |
29 |
Determine the null and alternative hypotheses.
A. H0: White and minority candidates have the same chance of passing the test.
H1: White and minority candidates do not have the same chance of passing the test.
B. H0: White and minority candidates do not have the same chance of passing the test.
H1: White and minority candidates have the same chance of passing the test.
C. H0: A white candidate is more likely to pass the test than a minority candidate.
H1: A white candidate is not more likely to pass the test than a minority candidate.
D. H0: A white candidate is not more likely to pass the test than a minority candidate.
H1: A white candidate is more likely to pass the test than a minority candidate.
Determine the test statistic.
Χ2 =_______ (Round to three decimal places as needed.)
Determine the P-value of the test statistic.
P-value = ____________(Round to four decimal places as needed.)
Is there sufficient evidence to support the claim that the results from the test are discriminatory?
A. There is not sufficient evidence to reject the claim that a white candidate is more likely to pass the test than a minority candidate.
B. There is not sufficient evidence to support the claim that the results are discriminatory.
C. There is sufficient evidence to support the claim that the results are discriminatory.
D. There is not sufficient evidence to reject the claim that a white candidate is more likely to pass the test than a minority candidate.
6) Many people believe that criminals who plead guilty tend to get lighter sentences than those who are convicted in trials. The accompanying table summarizes randomly selected sample data for defendants in burglary cases. All of the subjects had prior prison sentences. Use a 0.05 significance level to test the claim that the sentence (sent to prison or not sent to prison) is independent of the plea. If you were an attorney defending a guilty defendant, would these results suggest that you should encourage a guilty plea?
Click the icon to view the table.
Determine the null and alternative hypotheses.
A. H0: Pleading guilty reduces a defendant's chance of going to prison.
H1: Pleading guilty does not reduce a defendant's chance of going to prison.
B. H0: Pleading guilty does not reduce a defendant's chance of going to prison.
H1: Pleading guilty reduces a defendant's chance of going to prison.
C. H0: The sentence (sent to prison or not sent to prison) is independent of the plea.
H1: The sentence (sent to prison or not sent to prison) is not independent of the plea.
D. H0: The sentence (sent to prison or not sent to prison) is not independent of the plea.
H1: The sentence (sent to prison or not sent to prison) is independent of the plea.
Determine the test statistic.
Χ2 =______ (Round to three decimal places as needed.)
Determine the P-value of the test statistic.
P-value = ______(Round to four decimal places as needed.)
Use a 0.05 significance level to test the claim that the sentence (sent to prison or not sent to prison) is independent of the plea. If you were an attorney defending a guilty defendant, would these results suggest that you should encourage a guilty plea?
A. There is not sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results do not encourage pleas for guilty defendants.
B. There is sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results do not encourage pleas for guilty defendants. do not encourage
C. There is not sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results encourage pleas for guilty defendants.
D. There is sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results encourage pleas for guilty defendants.
3: More Info
|
|
Guilty Plea |
Not Guilty Plea |
|
Sent to Prison |
385 |
51 |
|
Not Sent to Prison |
575 |
51 |
7) The table below summarizes data from a survey of a sample of women. Using a 0.05 significance level, and assuming that the sample sizes of 900 men and 400 women are predetermined, test the claim that the proportions of agree/disagree responses are the same for subjects interviewed by men and the subjects interviewed by women. Does it appear that the gender of the interviewer affected the responses of women?
|
|
Gender of Interviewer |
|
|
|
Man |
Woman |
|
Woman who agree |
564 |
316 |
|
Woman who disagree |
336 |
84 |
Identify the null and alternative hypotheses. Choose the correct answer below.
A. H0: The response of the subject and the gender of the subject are independent.
H1: The response of the subject and the gender of the subject are dependent.
B. H0: The proportions of agree/disagree responses are different for the subjects interviewed by men and the subjects interviewed by women.
H1: The proportions are the same.
C. H0: The proportions of agree/disagree responses are the same for the subjects interviewed by men and the subjects interviewed by women.
H1: The proportions are different.
Compute the test statistic.
(Round to three decimal places as needed.)
Find the critical value(s).
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
What is the conclusion based on the hypothesis test?
(1) ______ H0. There (2) ________ sufficient evidence to warrant rejection of the claim that the proportions of agree/disagree responses are the same for subjects interviewed by men and the subjects interviewed by women. It (3) ________ that the gender of the interviewer affected the responses of women.
4: Chi-square distribution table
|
Area to the Right of the Critical Value |
|||||||||
|
Degrees of Freedom |
0.995 |
0.99 |
0.975 |
0.95 |
0.90 |
0.10 |
0.05 |
0.025 |
0.01 |
|
1 |
- |
- |
0.001 |
0.004 |
0.016 |
2.706 |
3.841 |
5.024 |
6.635 |
|
2 |
0.010 |
0.020 |
0.051 |
0.103 |
0.211 |
4.605 |
5.991 |
7.378 |
9.210 |
|
3 |
0.072 |
0.115 |
0.216 |
0.352 |
0.584 |
6.251 |
7.815 |
9.348 |
11.345 |
|
4 |
0.207 |
0.297 |
0.484 |
0.711 |
1.064 |
7.779 |
9.488 |
11.143 |
13.277 |
|
5 |
0.412 |
0.554 |
0.831 |
1.145 |
1.610 |
9.236 |
11.071 |
12.833 |
15.086 |
|
6 |
0.676 |
0.872 |
1.237 |
1.635 |
2.204 |
10.645 |
12.592 |
14.449 |
16.812 |
|
7 |
0.989 |
1.239 |
1.690 |
2.167 |
2.833 |
12.017 |
14.067 |
16.013 |
18.475 |
|
8 |
1.344 |
1.646 |
2.180 |
2.733 |
3.490 |
13.362 |
15.507 |
17.535 |
20.090 |
|
9 |
1.735 |
2.088 |
2.700 |
3.325 |
4.168 |
14.684 |
16.919 |
19.023 |
21.666 |
|
10 |
2.156 |
2.558 |
3.247 |
3.940 |
4.865 |
15.987 |
18.307 |
20.483 |
23.209 |
(1) Reject
Fail to reject
(2) is not
Is
(3) appears
Does not appears
8) The accompanying table shows results of challenged referee calls in a major tennis tournament. Use a 0.05 significance level to test the claim that the gender of the tennis player is independent of whether a call is overturned. Click the icon to view the table.
Determine the null and alternative hypotheses.
A. H0: The gender of the tennis player is independent of whether a call is overturned.
H1: The gender of the tennis player is not independent of whether a call is overturned.
B. H0: Male tennis players are more successful in overturning calls than female players.
H1: Male tennis players are not more successful in overturning calls than female players.
C. H0: Male tennis players are not more successful in overturning calls than female players.
H1: Male tennis players are more successful in overturning calls than female players.
D. H0: The gender of the tennis player is not independent of whether a call is overturned.
H1: The gender of the tennis player is independent of whether a call is overturned.
Determine the test statistic.
Χ2=______ (Round to three decimal places as needed.)
Determine the P-value of the test statistic.
P-value = ________ (Round to four decimal places as needed.)
Use a 0.05 significance level to test the claim that the gender of the tennis player is independent of whether a call is overturned. Choose the correct answer below.
A. There is sufficient evidence to warrant rejection of the claim that male tennis players are more successful in overturning calls than female tennis players.
B. There is not sufficient evidence to warrant rejection of the claim that male tennis players are more successful in overturning calls than female tennis players.
C. There is not sufficient evidence to warrant rejection of the claim that the gender of the tennis player is independent of whether a call is overturned.
D. There is not sufficient evidence to warrant rejection of the claim that the gender of the tennis player is independent of whether a call is overturned.
5: More Info
|
|
Was the challenge to the Call Successful? |
|
|
|
Yes |
No |
|
Men |
352 |
863 |
|
Woman |
366 |
787 |
9) In soccer, serious fouls result in a penalty kick with one kicker and one defending goalkeeper. The accompanying table summarizes results from 289 kicks during games among top teams. In the table, jump direction indicates which way the goalkeeper jumped, where the kick direction is from the perspective of the goalkeeper. Use a 0.01 significance level to test the claim that the direction of the kick is independent of the direction of the goalkeeper jump. Do the results support the theory that because the kicks are so fast, goalkeepers have no time to react, so the directions of their jumps are independent of the directions of the kicks?
Click the icon to view the penalty kick data.
Determine the null and alternative hypotheses.
A. H0: Jump direction is dependent on kick direction.
H1: Jump direction is independent of kick direction.
B. H0: Jump direction is independent of kick direction.
H1: Jump direction is dependent on kick direction.
C. H0: Goalkeepers do not jump in the direction of the kick.
H1: Goalkeepers jump in the direction of the kick.
D. H0: Goalkeepers jump in the direction of the kick.
H1: Goalkeepers do not jump in the direction of the kick.
Determine the test statistic.
Χ2=________ (Round to three decimal places as needed.)
Determine the P-value of the test statistic.
P-value = _______(Round to four decimal places as needed.)
Do the results support the theory that because the kicks are so fast, goalkeepers have no time to react, so the directions of their jumps are independent of the directions of the kicks?
There is (1)______ evidence to warrant rejection of the claim that the direction of the kick is independent of the direction of the goalkeeper jump. The results (2) _______ the theory that because the kicks are so fast, goalkeepers have no time to react.
6: Pentalty Kick Data
|
|
Goalkeeper Jump |
||
|
|
Left |
Center |
Jump |
|
Kick to Left |
59 |
4 |
39 |
|
Kick to Center |
40 |
11 |
32 |
|
Kick to Right |
41 |
5 |
58 |
(1) Sufficient
Insufficient
(2) Do not Support
Support
10) A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the accompanying table. Use a 0.05 significance level to test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample data?
Click the icon to view the data table.
Determine the null and alternative hypotheses.
A. H0: The amount of smoking is dependent upon seat belt use.
H1: The amount of smoking is not dependent upon seat belt use.
B. H0: The amount of smoking is independent of seat belt use.
H1: The amount of smoking is not independent of seat belt use.
C. H0: Heavy smokers are less likely than non-smokers to wear a seat belt.
H1: Heavy smokers are not less likely than non-smokers to wear a seat belt.
D. H0: Heavy smokers are not less likely than non-smokers to wear a seat belt.
H1: Heavy smokers are less likely than non-smokers to wear a seat belt.
Determine the test statistic.
Χ2 =______ (Round to three decimal places as needed.)
Determine the P-value of the test statistic.
P-Value = _______(Round to three decimal places as needed.)
Use a 0.05 significance level to test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample data?
A. There is not sufficient evidence to reject the claim that the amount of smoking is independent of seat belt use. The theory is not supported by the sample data.
B. There is sufficient evidence to reject the claim that heavy smokers are less likely than non-smokers to wear a seat belt. The theory is supported by the sample data.
C. There is not sufficient evidence to reject the claim that heavy smokers are less likely than non-smokers to wear a seat belt. The theory is supported by the sample data.
D. There is sufficient evidence to reject the claim that the amount of smoking is independent of seat belt use. The theory is not supported by the sample data.
7: More Info
|
|
Number of Cigarettes Smoked per Day |
|||
|
|
0 |
1-14 |
15-34 |
35 and over |
|
Wear Seat Belts |
159 |
13 |
44 |
8 |
|
Don’t Wear Seat Belts |
144 |
15 |
47 |
6 |
11) A poll was conducted to investigate opinions about global warming. The respondents who answered yes when asked if there is solid evidence that the earth is getting warmer were then asked to select a cause of global warming. The results are given in the accompanying data table. Use a 0.01 significance level to test the claim that the sex of the respondent is independent of the choice for the cause of global warming. Do men and women appear to agree, or is there a substantial difference?
|
|
Human activity |
Natural patterns |
Don’t know |
|
Male |
337 |
163 |
44 |
|
Female |
314 |
176 |
46 |
Click here to view the chi-square distribution table.
Identify the null and alternative hypotheses.
H0: (1) ________ and (2) _________ are (3) __________
H1: (4) ________ and (5) __________ are (6) _______
Compute the test statistic.
(Round to three decimal places as needed.)
Find the critical value(s).
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
What is the conclusion based on the hypothesis test?
(7) _______ H0 There (8) _________ sufficient evidence to warrant rejection of the claim that the sex of the respondent is independent of the choice for the cause of global warming. Men and women (9) _____ to agree.
8: Chi-square distribution table
|
Area to the Right of the Critical Value |
|||||||||
|
Degrees of Freedom |
0.995 |
0.99 |
0.975 |
0.95 |
0.90 |
0.10 |
0.05 |
0.025 |
0.01 |
|
1 |
- |
- |
0.001 |
0.004 |
0.016 |
2.706 |
3.841 |
5.024 |
6.635 |
|
2 |
0.010 |
0.020 |
0.051 |
0.103 |
0.211 |
4.605 |
5.991 |
7.378 |
9.210 |
|
3 |
0.072 |
0.115 |
0.216 |
0.352 |
0.584 |
6.251 |
7.815 |
9.348 |
11.345 |
|
4 |
0.207 |
0.297 |
0.484 |
0.711 |
1.064 |
7.779 |
9.488 |
11.143 |
13.277 |
|
5 |
0.412 |
0.554 |
0.831 |
1.145 |
1.610 |
9.236 |
11.071 |
12.833 |
15.086 |
|
6 |
0.676 |
0.872 |
1.237 |
1.635 |
2.204 |
10.645 |
12.592 |
14.449 |
16.812 |
|
7 |
0.989 |
1.239 |
1.690 |
2.167 |
2.833 |
12.017 |
14.067 |
16.013 |
18.475 |
|
8 |
1.344 |
1.646 |
2.180 |
2.733 |
3.490 |
13.362 |
15.507 |
17.535 |
20.090 |
|
9 |
1.735 |
2.088 |
2.700 |
3.325 |
4.168 |
14.684 |
16.919 |
19.023 |
21.666 |
|
10 |
2.156 |
2.558 |
3.247 |
3.940 |
4.865 |
15.987 |
18.307 |
20.483 |
23.209 |
(1) The sex of the respondent
The choice for human activity
Respondents who answered yes
(2) the respondents who answered no
the choice for natural patterns
the choice for the cause of global warming
(3) dependent.
independent.
(4) Respondents who answered yes
The choice for human activity
The sex of the respondent
(5) the respondents who answered no
the choice for natural patterns
the choice for the cause of global warming
(6) dependent.
independent.
(7) Fail to reject
Reject
(8) is
Is not
(9) Do not appear
Appear
12) A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the accompanying table. Using a 0.01 significance level, test the claim that injuries are independent of helmet color.
|
|
Color of Helmet |
||||
|
|
Black |
White |
Yellow |
Red |
Blue |
|
Controls (not injured) |
490 |
384 |
35 |
158 |
86 |
|
Cases (injured or killed) |
207 |
114 |
8 |
68 |
41 |
Click here to view the chi-square distribution table.
Identify the null and alternative hypotheses. Choose the correct answer below.
A. H0: Injuries and helmet color are dependent
H1: Injuries and helmet color are independent
B. H0: Injuries and helmet color are independent
H1: Injuries and helmet color are dependent
C. H0: Whether a crash occurs and helmet color are independent
H1: Whether a crash occurs and helmet color are dependent
D. H0: Whether a crash occurs and helmet color are dependent
H1: Whether a crash occurs and helmet color are independent
Compute the test statistic.
(Round to three decimal places as needed.)
Find the critical value(s).
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
What is the conclusion based on the hypothesis test?
(1) _________ H0. There (2) __________ sufficient evidence to warrant rejection of the claim that injuries are independent of helmet color.
9: Chi-square distribution table
|
Area to the Right of the Critical Value |
|||||||||
|
Degrees of Freedom |
0.995 |
0.99 |
0.975 |
0.95 |
0.90 |
0.10 |
0.05 |
0.025 |
0.01 |
|
1 |
- |
- |
0.001 |
0.004 |
0.016 |
2.706 |
3.841 |
5.024 |
6.635 |
|
2 |
0.010 |
0.020 |
0.051 |
0.103 |
0.211 |
4.605 |
5.991 |
7.378 |
9.210 |
|
3 |
0.072 |
0.115 |
0.216 |
0.352 |
0.584 |
6.251 |
7.815 |
9.348 |
11.345 |
|
4 |
0.207 |
0.297 |
0.484 |
0.711 |
1.064 |
7.779 |
9.488 |
11.143 |
13.277 |
|
5 |
0.412 |
0.554 |
0.831 |
1.145 |
1.610 |
9.236 |
11.071 |
12.833 |
15.086 |
|
6 |
0.676 |
0.872 |
1.237 |
1.635 |
2.204 |
10.645 |
12.592 |
14.449 |
16.812 |
|
7 |
0.989 |
1.239 |
1.690 |
2.167 |
2.833 |
12.017 |
14.067 |
16.013 |
18.475 |
|
8 |
1.344 |
1.646 |
2.180 |
2.733 |
3.490 |
13.362 |
15.507 |
17.535 |
20.090 |
|
9 |
1.735 |
2.088 |
2.700 |
3.325 |
4.168 |
14.684 |
16.919 |
19.023 |
21.666 |
|
10 |
2.156 |
2.558 |
3.247 |
3.940 |
4.865 |
15.987 |
18.307 |
20.483 |
23.209 |
(1) Fail to reject
Reject
(2) is
Is not
13) Fill in the blank.
A ________ is a table in which frequencies correspond to two variables.
A (1) ______ is a table in which frequencies correspond to two variables.
(1) relative frequency table
Contingency table
Pearson correlation coefficient table
Standard normal distribution table
14) Which of the following is NOT a requirement of conducting a hypothesis test for independence between the row variable and column variable in a contingency table?
Choose the correct answer below.
A. The sample data are randomly selected.
B. For every cell in the contingency table, the expected frequency, E, is at least 5.
C. The sample data are represented as frequency counts in a two-way table.
D. For every cell in the contingency table, the observed frequency, O, is at least 5.
15) Which of the following is NOT true for conducting a hypothesis test for independence between the row variable and column variable in a contingency table?
Choose the correct answer below.
A. The null hypothesis is that the row and column variables are independent of each other.
B. Small values of the c2 test statistic reflect significant differences between observed and expected frequencies.
C. Tests of independence with a contingency table are always right-tailed.
D. The number of degrees of freedom is (r-1)(c-1), where r is the number of rows and c is the number of columns.
16) Fill in the blank.
In a ____________ we test the claim that different populations have the same proportions of some characteristics.
In a (1) __________ we test the claim that different populations have the same proportions of some characteristics.
(1) test of homogeneity
McNemar’s test
Student t-test
Two-way analysis of variance
17) In a test of homogeneity, which of the following is NOT true?
Choose the correct answer below.
A. If the χ2 test statistic is large, the P-value will be small.
B. Small values of the χ2 test statistic would lead to a decision to reject the null hypothesis.
C. Samples are drawn from different populations and we wish to determine whether these populations have the same proportions of the characteristics being considered.
D. The null hypothesis is that the different populations have the same proportions of some characteristics.
1) The accompanying data table contains chest deceleration measurements (in g, where g is the force of gravity) from samples of small, midsize, and large cars. Shown are the technology results for analysis of variance of this data table. Assume that a researcher plans to use a 0.05 significance level to test the claim that the different size categories have the same mean chest deceleration in the standard crash test. Complete parts (a) and (b) below.
Click the icon to view the table of chest deceleration measurements
Click the icon to view the table of analysis of variance results.
a. What characteristic of the data specifically indicates that one-way analysis of variance should be used?
A. The measurements are categorized according to the one characteristic of size.
B. The population means are approximately normal.
C. There are three samples of measurements.
D. Nothing specifically indicates that one-way analysis of variance should be used.
b. If the objective is to test the claim that the three size categories have the same mean chest deceleration, why is the method referred to as analysis of variance?
A. The method is based on showing that the population variances are different.
B. The method is based on showing that the population variances are similar.
C. The method is based on estimates of multiple varying population variances.
D. The method is based on estimates of a common population variance.
1: More Info
Chest Deceleration Measurements (g) from a Standard Crash Test
|
Small |
44 |
39 |
37 |
54 |
39 |
44 |
42 |
|
Midsize |
36 |
53 |
43 |
42 |
52 |
49 |
41 |
|
Large |
32 |
45 |
41 |
38 |
37 |
38 |
33 |
2: More Info
|
SPSS Results |
Sum of Squares |
Df |
Mean Square |
F |
Sig. |
|
Between Groups |
200.857 |
2 |
100.429 |
3.288 |
0.061 |
|
Within Groups |
549.741 |
18 |
30.540 |
|
|
|
Total |
750.571 |
20 |
|
|
|
2) In a test of weight loss programs, 148 subjects were divided such that 37 subjects followed each of 4 diets. Each was weighed a year after starting the diet and the results are in the ANOVA table below. Use a 0.025 significance level to test the claim that the mean weight loss is the same for the different diets.
|
Source of Variation |
SS |
Df |
MS |
F |
P-value |
F crit |
|
Between Groups |
386.570 |
3 |
128.85652 |
4.0225 |
0.008771 |
3.208099 |
|
Within Groups |
4612.887 |
144 |
32.03394 |
|
|
|
|
Total |
4999.457 |
147 |
|
|
|
|
Should the null hypothesis that all the diets have the same mean weight loss be rejected?
A. Yes, because the P-value is less than the significance level.
B. No, because the P-value is less than the significance level.
C. Yes, because the P-value is greater than the significance level.
D. No, because the P-value is greater than the significance level.
3) Samples of pages were randomly selected from three different novels. The Flesch Reading Ease scores were obtained from each page, and the TI-83/84 Plus calculator results from analysis of variance are given below. Use a 0.05 significance level to test the claim that the three books have the same mean Flesch Reading Ease score.
Click the icon to view the TI-83/84 Plus calculator results.
What is the conclusion for this hypothesis test?
A. Reject H0. There is insufficient evidence to warrant the rejection of the claim that the three books have the same mean Flesch Reading Ease score.
B. Fail to reject H0. There is sufficient evidence to warrant the rejection of the claim that the three books have the same mean Flesch Reading Ease score.
C. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the three books have the same mean Flesch Reading Ease score.
D. Reject H0. There is sufficient evidence to warrant the rejection of the claim that the three books have the same mean Flesch Reading Ease score.
3. Calculator results
One-way ANOVA
F = 2.1187570412
p = 0.1353364549
Factor
df = 2
SS = 301.790248
¯ MS = 150.895124
One-way ANOVA
MS = 150.895124
Error
df = 35
SS = 2492.65452
MS = 71.2187007
Sxp = 8.43911729
4) If we use the amounts (in millions of dollars) grossed by movies in categories with PG, PG-13, and R ratings, we obtain the SPSS analysis of variance results shown below. Use a 0.01 significance level to test the claim that PG movies, PG13 movies, and R movies have the same mean gross amount.
Click the icon to view the SPSS results.
What is the conclusion for this hypothesis test?
A. Fail to reject H0. There is sufficient evidence to warrant the rejection of the claim that PG movies, PG-13 movies, and R movies have the same mean gross amount.
B. Fail to reject H0. There is evidence to warrant rejection of the claim that PG movies, PG-13 movies, and R movies have the same mean gross amount.
C. Reject H0. There is evidence to warrant the rejection of the claim that PG movies, PG13 movies, and R movies have the same mean gross amount.
D. Reject H0. There is insufficient evidence to warrant the rejection of the claim that PG movies, PG-13 movies, and R movies have the same mean gross amount.
4: SPSS result
|
Gross |
|||||
|
|
Sum of Squares |
Df |
Mean Square |
F |
Sig. |
|
Between Groups |
54698.674 |
2 |
27349.337 |
3.426 |
.044 |
|
Within Groups |
263434.9 |
33 |
7982.877 |
|
|
|
Total |
318133.6 |
35 |
|
|
|
5) A certain statistics instructor participates in triathlons. The accompanying table lists times (in minutes and seconds) he recorded while riding a bicycle for five laps through each mile of a 3-mile loop. Use a 0.05 significance level to test the claim that it takes the same time to ride each of the miles. Does one of the miles appear to have a hill?
Click the icon to view the data table of the riding times.
Determine the null and alternative hypotheses.
H0: (1) ________
H1: (2) _______
Find the F test statistic.
F = ______________ (Round to four decimal places as needed.)
Find the P-value using the F test statistic.
P-value = _________________ (Round to four decimal places as needed.)
What is the conclusion for this hypothesis test?
A. Reject H0. There is insufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time.
B. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the three different miles have the same mean ride time.
C. Reject H0. There is suffucient evidence to warrant rejection of the claim that the three different miles have the same mean ride time. Reject H0 sufficien
D. Fail to reject H0. There is evidence to warrant rejection of the claim that the three different miles have the same mean ride time.
Does one of the miles appear to have a hill?
A. Yes, these data suggest that the first mile appears to take longer, and a reasonable explanation is that it has a hill.
B. Yes, these data suggest that the second mile appears to take longer, and a reasonable explanation is that it has a hill.
C. Yes, these data suggest that the third and first miles appear to take longer, and a reasonable explanation is that they both have hills.
D. Yes, these data suggest that the third mile appears to take longer, and a reasonable explanation is that it has a hill.
E. No, these data do not suggest that any of the miles have a hill.
5: Riding Times (minutes and seconds)
Mile 1 3:15 3:24 3:23 3:23 3:22
Mile 2 3:19 3:22 3:22 3:16 3:20
Mile 3 3:35 3:32 3:28 3:32 3:28
(Note: when pasting the data into your technology, each mile row will have separate columns for each minute and second entry. You will need to convert each minute/second entry into seconds only.)
(1) m1 ¹ m2 ¹ m3
Exactly two of the population means are different from each other.
m1 = m2 = m3
m1 > m2 > m3
At least one of the three population means is different from the others.
(2) At least one of the three population means is different from the others.
m1 > m2 > m3
m1 = m2 = m3
m1 ¹ m2 ¹ m3
Exactly one of the three population means is different from the others.
6) Weights (kg) of poplar trees were obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the accompanying table. Use a 0.05 significance level to test the claim that the four treatment categories yield poplar trees with the same mean weight. Is there a treatment that appears to be most effective?
Click the icon to view the data table of the poplar weights.
Determine the null and alternative hypotheses.
H0: (1) ______
H1: (2) _______
Find the F test statistic.
F = ________ (Round to four decimal places as needed.)
Find the P-value using the F test statistic.
P-value = ___________(Round to four decimal places as needed.)
What is the conclusion for this hypothesis test?
A. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
B. Reject H0. There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
C. Reject H0. There is insufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
D. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the four different treatments yield the same mean poplar weight.
Is there a treatment that appears to be most effective?
A. No one treatment method seems to be most effective.
B. The 'Fertilizer and Irrigation' method seems to be most effective.
C. The 'Irrigation' method seems to be most effective.
D. The 'No Treatment' method seems to be most effective.
E. The 'Fertilizer' method seems to be most effective.
6: Poplar Weights (kg)
|
No Treatment |
Fertilizer |
Irrigation |
Fertilizer and Irrigation |
|
1.25 |
1.06 |
0.08 |
0.87 |
|
0.53 |
0.84 |
0.58 |
1.57 |
|
0.65 |
0.56 |
0.14 |
1.04 |
|
0.07 |
0.64 |
0.79 |
1.52 |
|
1.28 |
1.06 |
0.92 |
1.13 |
(1) At least two of the population means are equal.
Exactly two of the population means are equal.
Not all of the population means are equal.
m1 > m2 > m3 > m4
m1 = m2 = m3 = m4
m1 ¹ m2 ¹ m3 ¹ m4
(2) m1 = m2 = m3 = m4
At least two of the population means are equal.
Exactly two of the population means are different from the others.
m1 ¹ m2 ¹ m3 ¹ m4
At least one of the four population means is different from the others.
m1 > m2 > m3 > m4
7) Refer to the accompanying data table, which shows the amounts of nicotine (mg per cigarette) in king-size cigarettes, 100-mm menthol cigarettes, and 100-mm nonmenthol cigarettes. The king-size cigarettes are nonfiltered, while the 100-mm menthol cigarettes and the 100-mm nonmenthol cigarettes are filtered. Use a 0.05 significance level to test the claim that the three categories of cigarettes yield the same mean amount of nicotine. Given that only the king-size cigarettes are not filtered, do the filters appear to make a difference?
Click the icon to view the data table of the nicotine amounts.
Determine the null and alternative hypotheses.
H0: (1) ______
H1: (2) ______
Find the F test statistic.
F = ______________ (Round to four decimal places as needed.)
Find the P-value using the F test statistic.
P-value =______________ (Round to four decimal places as needed.)
What is the conclusion for this hypothesis test?
A. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.
B. Reject H0. There is insufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.
C. Reject H0. There is sufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.
D. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.
Do the filters appear to make a difference?
A. The results are inconclusive because the king-size cigarettes are a different size than the filtered cigarettes.
B. Given that the king-size cigarettes have the largest mean, it appears that the filters do make a difference (although this conclusion is not justified by the results from analysis of variance).
C. No, the filters do not appear to make a difference because there is sufficient evidence to warrant rejection of the claim.
D. No, the filters do not appear to make a difference because there is insufficient evidence to warrant rejection of the claim.
7: Nicotine amounts (mg)
|
King-Size |
100-mm Menthol |
100-mm Nonmenthol |
|||
|
Brand |
Nicotine (mg) |
Brand |
Nicotine (mg) |
Brand |
Nicotine (mg) |
|
1 |
1.3 |
1 |
1.2 |
1 |
0.4 |
|
2 |
1.2 |
2 |
1.0 |
2 |
1.1 |
|
3 |
1.0 |
3 |
1.1 |
3 |
0.6 |
|
4 |
1.1 |
4 |
0.9 |
4 |
1.1 |
|
5 |
1.4 |
5 |
1.3 |
5 |
1.1 |
|
6 |
1.3 |
6 |
1.4 |
6 |
0.7 |
|
7 |
1.2 |
7 |
0.9 |
7 |
1.1 |
|
8 |
1.0 |
8 |
1.2 |
8 |
1.1 |
|
9 |
1.3 |
9 |
1.2 |
9 |
0.9 |
|
10 |
1.1 |
10 |
0.8 |
10 |
1.0 |
(1) Exactly two of the population means are equal.
At least two of the population means are equal.
m1 = m2 = m3
m1 > m2 > m3
Not all of the population means are equal.
m1 ¹ m2 ¹ m3
(2) m1 > m2 > m3
m1 = m2 = m3
At least one of the three population means is different from the others.
m1 > m2 > m3
Exactly one of the three population means is different from the others.
8) Which of the following is NOT a property of the F distribution?
Choose the correct answer below.
A. Values in the F distribution cannot be negative.
B. The F distribution is bell shaped.
C. The F distribution is not symmetric.
D. The exact shape of the F distribution depends on the two different degrees of freedom.
9) Fill in the blank.
The method of ___ is used for tests of hypothesis that three or more population means are equal.
The method of (1) ________ is used for tests of hypotheses that three or more population means are equal.
(1) confidence intervals
A survey
A chi-square distribution
One-way analysis of variance
10. Fill in the blank.
A ______ is a characteristic used in ANOVA that allows us to distinguish different population from one another.
A (1) ________ is a characteristic used in ANOVA that allows us to distinguish different populations from one another.
(1) Standard deviation
Control chart
Treatment
Residual
11. Which of the following is NOT a requirement for using one-way analysis of variance for testing equality of three or more population means?
Choose the correct answer below.
A. The different samples are from populations that are categorized in only one way.
B. The populations have distributions that are approximately normal.
C. The samples are simple random samples of quantitative data.
D. The samples are matched or paired in some way
12) Which of the following is NOT true when using one-way analysis of variance for testing equality of three or more population means?
Choose the correct answer below.
A. The conclusion that there is sufficient evidence to reject the claim of equal population means does not indicate a particular mean is different from the others.
B. Small F test statistics indicate that the decision is to reject the null hypothesis of equal means.
C. Small P-values indicate that the decision is to reject the null hypothesis of equal means.
D. The numerator of the F test statistic measures variation between sample means.
13) Which of the following is NOT true?
Choose the correct answer below.
A. When testing for equality of three population means, do not use multiple hypothesis tests with two samples at a time.
B. If the decision from ANOVA is to reject the equality of the three population means, the particular mean that differs from the others is known.
C. As the number of tests of significance increase, the risk of finding a difference by chance alone increases.
D. The F test statistic is very sensitive to sample means, even though it is obtained through two different estimates of the common population variance.
14) Which of the following is NOT true of the F test statistic?
Choose the correct answer below.
A. F = (variance between samples)/(variance with samples)
B. F = MS (treatment)/MS(error) ,when testing with unequal sample sizes MS(treatment) MS(error)
C. If the F test statistic is large, then the P-value will be large.
D. The F test statistic is never negative.
15) Which of the following is NOT true of one-way analysis of variance experimental design?
Choose the correct answer below.
A. Using a rigorously controlled design is one way to reduce the effect of extraneous factors.
B. In any design, if the conclusion is that the differences among the means are significant, the differences are explained by the factor used.
C. Good results require that experiments be carefully designed and executed.
D. A completely randomized experimental design is one way to reduce the effect of extraneous factors.
16) Which of the following is NOT a procedure (either formal or informal) to use to identify the specific means that are different when the conclusion of a one-way ANOVA is that at least one of the population means is different?
Choose the correct answer below.
A. Construct boxplots of the data sets to see if one or more is significantly different from the others.
B. Utilize Bayes' Theorem to differentiate at least one mean from the others.
C. Utilize multiple comparison tests that make adjustments to overcome the problem of increasing the probability of a Type I error.
D. Use a range test to identify subsets of means that are not significantly different from each other.
1) The accompanying data table lists results from car crash tests. Included in results from car crash tests are loads (pounds) on the left femur and right femur, and those values are shown in the table below. What characteristic of the data suggests that the appropriate method of analysis is two-way analysis of variance? That is, what is "two-way" about the data entered in the table?
Click on the icon to view the data table.
Choose the correct answer below.
A. The load values are categorized using two different factors of femur (left or right) and size of car (small, midsize, or large).
B. There are two possibilities for the femur, either left or right.
C. The data is measured in pounds, part of the imperial system, which is inherently two-way.
D. In this case, the appropriate method of analysis is not two-way analysis of variance.
1: Car Crash Test Data
|
|
Small |
Midsize |
Large |
|
|
Left Femur |
1194 |
398 |
214 |
Left Femur |
|
288 |
319 |
1633 |
||
|
331 |
303 |
735 |
||
|
707 |
297 |
883 |
||
|
600 |
807 |
942 |
||
|
244 |
279 |
884 |
||
|
336 |
410 |
473 |
||
|
Right Femur |
1266 |
846 |
754 |
Right Femur |
|
324 |
717 |
1201 |
||
|
445 |
134 |
774 |
||
|
1052 |
237 |
556 |
||
|
1478 |
690 |
667 |
||
|
1041 |
907 |
557 |
||
|
454 |
550 |
291 |
||
|
|
Small |
Midsize |
Large |
|
2) Researchers randomly select and weigh men and women. Their weights are entered in the table below, so that each cell includes five weights. Is the result a balanced design? Why or why not?
Age
|
|
Under 30 |
30 - 40 |
Over 40 |
|
Female |
114.8, 127.1, 108.8, 106.7, 124.3 |
149.3, 127.1, 110.2 126.0, 149.9 |
160.1, 181.2, 255.9 163.1, 162.8 |
|
Male |
144.2, 156.3, 151.3, 161.9, 151.8 |
175.8, 204.6, 169.8 198.0, 166.1 |
169.1, 139.0, 103.3 172.9, 214.5 |
Choose the correct answer below.
A. Yes; the sample values are categorized in two ways.
B. Yes; each cell contains the same number of sample values.
C. No; each cell contains an odd number of sample values.
D. No; there are a different number of columns and rows.
3) The following table shows the two-way ANOVA output for the weights of poplar trees. Test the hypothesis that the weights of poplar trees are not affected by an interaction between site and treatment.
Source DF SS MS F P
Site 3 0.9893 0.329752 1.51 0.225
Treatment 1 0.0611 0.061146 0.28 0.599
Interaction 3 2.1620 0.720651 3.30 0.028
Error 48 10.4822 0.218379
Total 55 13.6946
Is there evidence to support the claim of interaction? (Assume a 0.05 significance level.)
A. Since the P-value for interaction is small, there is no evidence of interaction.
B. Since the P-value for interaction is large, there is no evidence of interaction.
C. Since the P-value for interaction is small, there is evidence of interaction.
D. Since the P-value for interaction is large, there is evidence of interaction.
4) Use the technology display, which results from the head injury measurements from car crash dummies listed below. The measurements are in hic (head injury criterion) units, and they are from the same cars used for the table below. Use a 0.05 significance level to test the given claim.
Test the null hypothesis that head injury measurements are not affected by an interaction between the type of car (foreign, domestic) and size of the car (small, medium, large). What do you conclude?
Click the icon to view the data table and technology display.
What are the null and alternative hypotheses?
A. H0: Head injury measurements are affected by an interaction between type of car and size of the car.
H1: Head injury measurements are not affected by an interaction between type of car and size of the car.
B. H0: Head injury measurements are not affected by an interaction between type of car and size of the car.
H1: Head injury measurements are affected by an interaction between type of car and size of the car.
C. H0: Head injury measurements are not affected by type of car.
H1: Head injury measurements are affected by type of car.
D. H0: Head injury measurements are not affected by size of car.
H1: Head injury measurements are affected by size of car.
Find the test statistic.
F = _________(Round to two decimal places as needed.)
Determine the P-value.
P-value = ________(Round to three decimal places as needed.)
Determine whether there is sufficient evidence to support the given alternative hypothesis.
Since the P-value is (1) _________0.05, (2) _____________ H0 There is (3) _______________ evidence to
Support the alternative hypothesis. Conclude that there (4) ___________appear to be an effect from an interaction between the type of car (foreign or domestic) and whether the car is small, medium, or large.
2: Data Table
|
Size of Car |
|||
|
|
Small |
Medium |
Large |
|
Foreign |
292 |
244 |
355 |
|
|
533 |
512 |
670 |
|
|
505 |
399 |
337 |
|
Domestic |
405 |
473 |
212 |
|
|
377 |
365 |
329 |
|
|
371 |
348 |
164 |
|
Source DF SS MS F P Type 1 35823 35822.7 2.60 0.133 Size 2 14905 7452.7 0.54 0.596 Interaction 2 41500 20750.2 1.51 0.261 Error 12 165354 13779.5 Total 17 257583 |
(1) Less than or equal to
Greater than
2) fail to reject
Reject
3) sufficient
Insufficient
4) does not
Does
5) The accompanying data table lists measures of self-esteem from a student project. The objective of the project was to study how levels of self-esteem in subjects relate to their perceptions of self-esteem in other target people who were described in writing. The test here works well even though the data are at the ordinal level of measurement. Use a 0.05 significance level and apply the methods of two-way analysis of variance. What is the conclusion?
Click on the icon to view the data table.
State the null and alternative hypotheses in the test for the effect of an interaction between row and column factors.
H0: There (1) ________________ interaction between the subject's self-esteem and the target's self-esteem in determining self-esteem measures.
H1: There (2) _________________ interaction between the subject's self-esteem and the target's self-esteem in determining self-esteem measures.
What is the value of the test statistic for this test?
F = _______________(Round to two decimal places as needed.)
What is the corresponding P-value of the test statistic, F, for this test?
P-value = ___________(Round to three decimal places as needed.)
State the conclusion of this test.
(3)___________H0. There (4)________________ sufficient evidence to warrant rejection of the claim that measurems of self-esteem are not affected by an interaction between the subject's self-esteem and the target's selfesteem. There (5)____________ appear to be an effect from an interaction between the self-esteem of the subject and the perception of the self-esteem of the target.
State the null and alternative hypotheses in the test for the effect from the row factor.
A. H0: The row values are from populations with the same standard deviation.
H1: At least one of the rows is sampled from a population with a standard deviation different from the others.
B. H0: At least one of the rows is sampled from a population with a mean different from the others.
H1: The row values are from populations with the same mean.
C. H0: The row values are from populations with the same mean.
H1: At least one of the rows is sampled from a population with a mean different from the others.
D. In this case, the test for the effect from a row factor should not be done.
What is the value of the test statistic for this test?
A. F = ____________(Round to two decimal places as needed.)
B. In this case, the test for the effect from a row factor should not be done.
What is the corresponding P-value of the test statistic, F, for this test?
A. P-value = _______________(Round to three decimal places as needed.)
B. In this case, the test for the effect from a row factor should not be done.
State the conclusion of this test.
A. Do not reject H0. There is insufficient evidence to warrant rejection of the claim that the row values are from populations with the same standard deviation.
B. Do not reject H0. There is insufficient evidence to warrant rejection of the claim that the row values are from populations with the same mean.
C. Reject H0. There is sufficient evidence to warrant rejection of the claim that the row values are from populations with the same mean.
D. Reject H0. There is sufficient evidence to warrant rejection of the claim that the row values are from populations with the same standard deviation.
E. In this case, the test for the effect from a row factor should not be done.
State the null and alternative hypotheses in the test for the effect from the column factor.
A. H0: At least one of the columns is sampled from a population with a mean different from the others.
H1: The column values are from populations with the same mean.
B. H0: The column values are from populations with the same mean.
H1: At least one of the columns is sampled from a population with a mean different from the others.
C. H0: The column values are from populations with the same standard deviation.
H1: At least one of the columns is sampled from a population with a standard deviation different from the others.
D. In this case, the test for the effect from a column factor should not be done.
What is the value of the test statistic for this test?
A. F = _________________(Round to two decimal places as needed.)
B. In this case, the test for the effect from a column factor should not be done.
What is the corresponding P-value of the test statistic, F, for this test?
A. P-value = ___________(Round to three decimal places as needed.)
B. In this case, the test for the effect from a column factor should not be done.
State the conclusion of this test.
A. Reject H0. There is sufficient evidence to warrant rejection of the claim that the column values are from populations with the same standard deviation.
B. Reject H0. There is sufficient evidence to warrant rejection of the claim that the column values are from populations with the same mean.
C. Do not reject H0. There is insufficient evidence to warrant rejection of the claim that the column values are from populations with the same mean.
D. Do not reject H0. There is insufficient evidence to warrant rejection of the claim that the column values are from populations with the same standard deviation.
E. In this case, the test for the effect from a column factor should not be done.
3: Self – esteem Measures for Subject and Target
|
|
Subject’s self – esteem |
||||||
|
Low |
Medium |
High |
|||||
|
Target’s Self-esteem
|
Low |
5 |
4 |
3 |
3 |
2 |
1 |
|
4 |
4 |
3 |
4 |
2 |
2 |
||
|
3 |
3 |
4 |
3 |
2 |
5 |
||
|
5 |
4 |
4 |
4 |
3 |
3 |
||
|
5 |
4 |
2 |
2 |
3 |
3 |
||
|
5 |
5 |
2 |
3 |
3 |
2 |
||
|
High |
2 |
2 |
4 |
3 |
3 |
2 |
|
|
4 |
2 |
1 |
2 |
3 |
2 |
||
|
2 |
3 |
1 |
3 |
3 |
4 |
||
|
2 |
4 |
2 |
4 |
3 |
4 |
||
|
2 |
2 |
3 |
1 |
4 |
3 |
||
|
2 |
3 |
1 |
4 |
3 |
4 |
||
1) is no
Is an
2) is no
Is an
3) Fail to reject
Reject
4) is not
Is
5) does not
Does
6) The accompanying table lists pulse rates. Use a 0.05 significance level and apply the methods of two-way analysis of variance. What is the conclusion?
Click on the icon to view the data table.
State the null and alternative hypotheses in the test for the effect of an interaction between row and column factors.
H0: There (1) ________________ interaction between gender and age.
H1: There (2) _________________ interaction between gender and age.
What is the value of the test statistic for this test?
F = ________________________(Round to two decimal places as needed.)
What is the corresponding P-value of the test statistic, F, for this test?
P-value = _________________ (Round to three decimal places as needed.)
State the conclusion of this test.
(3) ____________ H0. There (4)____________________ sufficient evidence to warrant rejection of the claim that pulse rates are not affected by an interaction between gender and age. There (5) ________________appear to be an effect from an interaction between gender and age.
State the null and alternative hypotheses in the test for the effect from the row factor.
A. H0: The row values are from populations with the same mean.
H1: At least one of the rows is sampled from a population with a mean different from the others.
B. H0: The row values are from populations with the same standard deviation.
H1: At least one of the rows is sampled from a population with a standard deviation different from the others.
C. H0: At least one of the rows is sampled from a population with a mean different from the others.
H1: The row values are from populations with the same mean.
D. In this case, the test for the effect from a row factor should not be done.
What is the value of the test statistic for this test?
A. F = ___________________(Round to two decimal places as needed.)
B. In this case, the test for the effect from a row factor should not be done.
What is the corresponding P-value of the test statistic, F, for this test?
A. P-value = ________________(Round to three decimal places as needed.)
B. In this case, the test for the effect from a row factor should not be done.
State the conclusion of this test. Choose the correct answer below.
A. Do not reject H0. There is insufficient evidence to warrant rejection of the claim that the row values are from populations with the same mean.
B. Reject H0. There is sufficient evidence to warrant rejection of the claim that the row values are from populations with the same mean.
C. Reject H0. There is sufficient evidence to warrant rejection of the claim that the row values are from populations with the same standard deviation.
D. Do not reject H0. There is insufficient evidence to warrant rejection of the claim that the row values are from populations with the same standard deviation.
E. In this case, the test for the effect from a row factor should not be done.
State the null and alternative hypotheses in the test for the effect from the column factor.
A. H0: The column values are from populations with the same standard deviation.
H1: At least one of the columns is sampled from a population with a standard deviation different from the others.
B. H0: The column values are from populations with the same mean.
H1: At least one of the columns is sampled from a population with a mean different from the others.
C. H0: At least one of the columns is sampled from a population with a mean different from the others.
H1: The column values are from populations with the same mean.
D. In this case, the test for the effect from a column factor should not be done.
What is the value of the test statistic for this test?
A. F = ____________________(Round to two decimal places as needed.)
B. In this case, the test for the effect from a column factor should not be done.
What is the corresponding P-value of the test statistic, F, for this test?
A. P-value = ___________________(Round to three decimal places as needed.)
B. In this case, the test for the effect from a column factor should not be done.
State the conclusion of this test.
A. Reject H0. There is sufficient evidence to warrant rejection of the claim that the column values are from populations with the same standard deviation.
B. Do not reject H0. There is insufficient evidence to warrant rejection of the claim that the column values are from populations with the same standard deviation.
C. Do not reject H0. There is insufficient evidence to warrant rejection of the claim that the column values are from populations with the same mean.
D. Reject H0. There is sufficient evidence to warrant rejection of the claim that the column values are from populations with the same mean.
E. In this case, the test for the effect from a column factor should not be done
4: Pulse Rates for Gender and Age
|
Under 30 Years of Age |
Over 30 Years of Age |
||
|
Female |
78 105 79 63 61 97 81 99 91 97 |
76 76 72 66 73 77 61 73 75 56 |
Female |
|
Male |
60 80 56 69 69 74 75 68 63 56 |
46 71 61 67 90 80 59 58 64 59 |
Male |
1) is no
Is an
2) is no
Is an
3) Fail to reject
Reject
4) is not
Is
5) does
Does not
7) Fill in the blank.
There is an _______ between two factors if the effect of one of the factors changes for different categories of the other factor.
There is an (1) _________________ between two factors if the effect of one of the factors changes for different categories of the other factor.
1) Interaction
Unusual relationship
Outlier
Equality relation
8) Which of the following is NOT a requirement for using two-way analysis of variance to test for an interaction effect, an effect from the row factor, and an effect from the column factor?
Choose the correct answer below.
A. The samples are independent of each other.
B. For each cell, the sample comes from a population that is approximately normal.
C. The sample values are categorized two ways.
D. The samples are simple random samples of categorical data
9) Which of the following is not a step in the procedure for two-way ANOVA to test for an interaction effect, an effect from the row factor, and an effect from the column factor?
Choose the correct answer below.
A. If the P-value is small, reject the null hypothesis of no interaction. Conclude that there is an interaction effect.
B. If the P-value is large, reject the null hypothesis of no interaction. Conclude that there is an interaction effect.
C. If the conclusion is that there is no interaction effect, then proceed to test for the effect from the row factor and the effect from the column factor.
D. Begin by testing the hypothesis that there is no interaction between the two factors.
Please download the answer file using this link
https://drive.google.com/file/d/1bjiHY10v7bkWWOW8p9NFMxDGVH9utIAq/view?usp=sharing
