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1)The chi-square test requires that each expected frequency be equal to or greater than what? number?
The sampling distribution for the difference in proportions is the result of subtracting one sampling distribution for the proportion from a second sampling distribution for the proportion
1)The chi-square test requires that each expected frequency be equal to or greater than what? number?
The sampling distribution for the difference in proportions is the result of subtracting one sampling distribution for the proportion from a second sampling distribution for the proportion
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1)The chi-square test requires that each expected frequency be equal to or greater than what? number?
- The sampling distribution for the difference in proportions is the result of subtracting one sampling distribution for the proportion from a second sampling distribution for the proportion.
- "Gamers" are described as people who regularly play video games. A random sample of 120 people was selected and 66 were found to be male. Using this? sample, what is the point estimate for the proportion of gamers who are?male?
- A Type II error is known as the? consumer's risk? because, when it occurs in quality control? settings, the customer is getting a product from a process that is not performing properly.
- The null hypothesis for a? chi-square goodness-of-fit test always states that the stated distribution is followed.
- The standard error of the difference between two means describes the variation in the difference between two sample means.
- A benefit of point estimates is that they provide information about their accuracy.
- Lisa is a regional manager for a restaurant chain that has locations in the towns of? Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location. What is the expected frequency of satisfied customers from the Berwick? sample?
| |
Berwick
|
Milton
|
Leesburg
|
|
Number Satisfied
|
80
|
85
|
60
|
|
Sample Size
|
100
|
120
|
80
|
|
|
|
|
|
- For a? one-tail (upper) hypothesis? test, if the? z- or? t-test statistic exceeds the critical? value, we do not reject the null hypothesis.
- The rejection region for the? chi-square test to compare two or more population proportions lies on the right tail of the? chi-square distribution.
- Given that a? 95% confidence interval is? (6.5, 12.5), we can state that we are? 95% confident that the population mean is between 6.5 and 12.5.
- A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam is equal to 45? minutes; a Type II error would occur if the professor concludes that the average exam time is? _______.
- When calculating a confidence interval for the mean using a sample size of 30 or more with a known population standard? deviation, the? ________ is used.
- The alternative? hypothesis, denoted by H1?,represents the opposite of the null hypothesis and is believed to be if the null hypothesis is found to be .
- The null? hypothesis, denoted by H0?,represents the status quo and involves stating the belief that the population parameter is,less than or equals≤?,equals=?, or greater than or equals≥a specific value.
- Because hypothesis testing relies on a? sample, there exists risk that the conclusions about the population will be wrong because of a sampling error.
- The? ________ frequencies refer to the sample data collected from a population of interest when performing a hypothesis test comparing two or more population proportions.
- The standard error of the proportion measures the average variation around the mean of the sample proportions taken from the population.
- The point estimate for the population mean will always be found within the limits of the confidence interval for the mean.
- If the hypothesis test is used in a quality control? setting, the alternative hypothesis takes the stance that the process is not behaving as it should and needs some sort of attention.
- A gaming company would like to test the hypothesis that the average age of someone who uses gaming console A is different from the average age of someone who uses gaming console B. A random sample of 36 gaming console A users had an average age of 34.2 years while a random sample of 30 gaming console B users had an average age of 32.7 years. Assume that the population standard deviation for the age of gaming console A and gaming console B users is 3.9 and 4.0? years, respectively. What is the? 90% confidence interval for the difference in population? means?
- An insurance company would like to perform a? chi-square test to investigate whether a difference exists in the proportion of male and female teenagers who text while they drive. A random sample of 80 male teenagers found that 50 indicated they texted while driving. A random sample of 120 female teenagers found that 65 indicated they texted while driving. How many degrees of freedom does the? chi-square critical value? have?
- Lisa is a regional manager for a restaurant chain that has locations in the towns of? Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location. What is the expected frequency of satisfied customers from the Milton? sample?
| |
Berwick
|
Milton
|
Leesburg
|
|
Number Satisfied
|
80
|
85
|
60
|
|
Sample Size
|
100
|
120
|
80
|
|
- A golfer claims that his average golf score at the course he plays regularly is less than 90. What is the correct hypothesis statement for this golfer to prove his? claim? B.
- A hypothesis is an assumption about a population parameter such as a mean or a proportion.
- When calculating a confidence interval for? proportions, we assume that proportion data follow the? ________.
- When performing a hypothesis test to compare two or more population? proportions, the test statistic follows which? distribution?
- A phone company would like to estimate the proportion of households that use cell phones for their phone service without a land line. A random sample of 150 households was selected and 48 relied strictly on cell phones for their service. Using this? sample, what is the point estimate for the proportion of households without land? lines?
- The purpose of generating a confidence interval for the mean is to provide an estimate for the value of the population mean.
- The standard error of the difference between two means describes the variation in the difference between two sample means.
- Suppose a chain restaraunt has run a major advertising campaign in the hopes of increasing monthly sales. To investigate the effectiveness of this? campaign, the restaraunt randomly selected six different locations and recorded the monthly sales before and after the advertising. The following data represents these sales figures in thousands of dollars. Assume Population 1 is defined as sales after the advertising campaign and Population 2 is defined as sales before the advertising campaign. What is the mean of the? matched-pair differences?
|
Restaurant
|
1
|
2
|
3
|
4
|
5
|
6
|
|
After
|
$123
|
$122
|
$145
|
$156
|
$160
|
$134
|
|
Before
|
$107
|
$110
|
$143
|
$168
|
$145
|
$125
|
|
|
|
|
|
|
|
|
|
|
|
|
- A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam is equal to 45 minutes. What is the correct hypothesis? statement?
- The definition of a? 90% confidence interval is that we expect that close to? 90% of a large number of sample means drawn from a population will produce confidence intervals that include that? population's mean.
- A gaming software agency would like to test if the average age of? "gamers" (those that routinely play video? games) is more than 30 years old. What is the correct hypothesis? statement?
- A? ________ for the mean is an interval estimate around a sample mean that provides us with a range of where the population mean lies.
- A government agency would like to investigate if a difference exists in the proportion of flights that arrive? on-time between Airline? A, Airline? B, Airline? C, and Airline D. The following data represent the number of? on-time flights from random samples taken from each airline. How many degrees of freedom does the? chi-square critical value? have?
| |
A
|
B
|
C
|
D
|
|
Number? On-time
|
90
|
95
|
85
|
60
|
|
Sample Size
|
100
|
120
|
100
|
80
|
- The critical value for a hypothesis test? _______.
- When conducting a hypothesis test comparing two populations with independent? samples, the sample sizes must be equal.
- A government agency would like to investigate if a difference exists in the proportion of flights that arrive? on-time between Airline? A, Airline? B, Airline? C, and Airline D. The following data represent the number of? on-time flights from random samples taken from each airline. What is the expected frequency of? on-time flights from the Airline A? sample?
| |
A
|
B
|
C
|
D
|
|
Number? On-time
|
90
|
95
|
85
|
60
|
|
Sample Size
|
100
|
120
|
100
|
80
|
- Because hypothesis testing relies on a? sample, there exists risk that the conclusions about the population will be wrong because of a sampling error.
QUIZ 3
- A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam has a standard deviation that is less than 5.0 minutes. Which of the following would be the correct hypothesis? statement?
- If the null hypothesis is for? one-way ANOVA, the mean square total? (MST) would be a good estimate for the? _______.
- A smaller standard error of the slope increases the likelihood that we can establish a significant relationship between the independent and dependent variables.
- Consider the partially completed randomized block ANOVA summary table.
|
Source
|
Sum of
Squares
|
Degrees of
Freedom
|
Mean Sum of
Squares
|
F
|
|
Between
|
600
|
3
|
|
|
|
Block
|
|
5
|
|
|
|
Error
|
750
|
|
|
|
|
Total
|
?2,150
|
23
|
|
|
What is the degrees of freedom for the sum of squares error for this ANOVA? procedure?
- Consider the partially completed? two-way ANOVA summary table.
|
Source
|
Sum of
Squares
|
Degrees of
Freedom
|
Mean Sum
of Squares
|
F
|
|
Factor B
|
|
2
|
|
|
|
Factor A
|
600
|
|
200
|
|
|
Interaction
|
144
|
|
|
|
|
Error
|
384
|
12
|
|
|
|
Total
|
?1,288
|
23
|
|
|
What is the mean sum of squares for Factor B for this ANOVA? procedure?
- Consider the partially completed? one-way ANOVA summary table.
|
Source
|
Sum of Squares
|
Degrees of
Freedom
|
Mean Sum
of Squares
|
F
|
|
Between
|
270
|
|
|
|
|
Within
|
|
18
|
|
|
|
Total
|
810
|
21
|
|
|
What is the degrees of freedom for the sum of squares between for this ANOVA? procedure?
- A dependent? variable, x, explains the variation in another? variable, which is called the independent? variable, y.
- With? one-way ANOVA, there will be a greater chance of rejecting the null hypothesis when more variation in the data is due to the SSB rather than the SSW.
- The technique of? ________ enables us to describe a straight line that best fits a series of ordered pairs? (x,y).
- ?Two-way ANOVA incorporates a blocking factor to account for variation outside of the main factor in the hopes of increasing the likelihood of detecting a variation due to the main factor.
- A coefficient of determination equal to zero indicates that there is no relationship between the independent and dependent variables.
- Consider the partially completed randomized block ANOVA summary table.
|
Source
|
Sum of
Squares
|
Degrees of
Freedom
|
Mean Sum of
Squares
|
F
|
|
Between
|
600
|
3
|
|
|
|
Block
|
|
5
|
|
|
|
Error
|
750
|
|
|
|
|
Total
|
?2,150
|
23
|
|
|
What is the sum of squares block for this ANOVA? procedure?
- Consider the partially completed? one-way ANOVA summary table.
|
Source
|
Sum of Squares
|
Degrees of
Freedom
|
Mean Sum
of Squares
|
F
|
|
Between
|
270
|
|
|
|
|
Within
|
|
18
|
|
|
|
Total
|
810
|
21
|
|
|
What is the ?F-test statistic for this ANOVA? procedure?
- Consider the relationship between household income and square footage of the primary residence. Determine whether the following statement is .Household income would be considered the independent variable.
- A video website would like to test the hypothesis that the standard deviation for the length of an online video watched by a user is more than 2 minutes. A random sample of 21 people who watched online videos was selected. The sample standard deviation for the length of the video was found to be 2.5 minutes. What is the number of degrees of freedom for this hypothesis? test?
- The? ________ measures the total variation in the dependent variable in simple regression analysis.
- An assumption of regression analysis is that the relationship between the independent and dependent variables is linear.
- A factor in an ANOVA test describes the cause of the variation in the data.
- Consider the partially completed? two-way ANOVA summary table.
|
Source
|
Sum of
Squares
|
Degrees of
Freedom
|
Mean Sum
of Squares
|
F
|
|
Factor B
|
|
2
|
|
|
|
Factor A
|
600
|
|
200
|
|
|
Interaction
|
144
|
|
|
|
|
Error
|
384
|
12
|
|
|
|
Total
|
?1,288
|
23
|
|
|
What is the sum of squares for Factor B for this ANOVA? procedure?
- The? _______ provides an estimate for the population variance if the null hypothesis is for? one-way ANOVA.
- A relationship is linear if the scatter plot of the independent and dependent variables has a? straight-line pattern.
- Consider the partially completed? two-way ANOVA summary table.
|
Source
|
Sum of
Squares
|
Degrees of
Freedom
|
Mean Sum
of Squares
|
F
|
|
Factor B
|
|
2
|
|
|
|
Factor A
|
600
|
|
200
|
|
|
Interaction
|
144
|
|
|
|
|
Error
|
384
|
12
|
|
|
|
Total
|
?1,288
|
23
|
|
|
How many Factor B populations are being compared for this ANOVA? procedure?
- Consider the partially completed randomized block ANOVA summary table.
|
Source
|
Sum of
Squares
|
Degrees of
Freedom
|
Mean Sum of
Squares
|
F
|
|
Between
|
600
|
3
|
|
|
|
Block
|
|
5
|
|
|
|
Error
|
750
|
|
|
|
|
Total
|
?2,150
|
23
|
|
|
What is the mean square block for this ANOVA? procedure?
- If the confidence interval for the regression slope includes? zero, we would have some evidence that betaβ could be equal to? zero, which would indicate that there may not be a relationship between the dependent and independent variables.
- The? ________ indicates both the strength and direction of the linear relationship between the independent and dependent variables.
- ?A(n) _______ in ANOVA describes the cause of the variation in the data.
- The mean square within? (MSW) provides a good estimate of the population variance only if the null hypothesis is .
- The degrees of freedom for the critical value for a hypothesis test for a single population variance is n−?2, where n is the sample size
- Consider the partially completed? one-way ANOVA summary table.
|
Source
|
Sum of Squares
|
Degrees of
Freedom
|
Mean Sum
of Squares
|
F
|
|
Between
|
270
|
|
|
|
|
Within
|
|
18
|
|
|
|
Total
|
810
|
21
|
|
|
What is the number of populations being compared for this ANOVA? procedure?
- A Type I error occurs when performing? one-way ANOVA when we conclude that the? _______.
- Consider the partially completed randomized block ANOVA summary table.
|
Source
|
Sum of
Squares
|
Degrees of
Freedom
|
Mean Sum of
Squares
|
F
|
|
Between
|
600
|
3
|
|
|
|
Block
|
|
5
|
|
|
|
Error
|
750
|
|
|
|
|
Total
|
?2,150
|
23
|
|
|
How many main factor populations are being compared for this ANOVA? procedure?
- Consider the partially completed? two-way ANOVA summary table.
|
Source
|
Sum of
Squares
|
Degrees of
Freedom
|
Mean Sum
of Squares
|
F
|
|
Factor B
|
|
2
|
|
|
|
Factor A
|
600
|
|
200
|
|
|
Interaction
|
144
|
|
|
|
|
Error
|
384
|
12
|
|
|
|
Total
|
?1,288
|
23
|
|
|
The degrees of freedom for the interaction of factors A and B for this ANOVA procedure is? __
- Consider the partially completed? two-way ANOVA summary table.
|
Source
|
Sum of
Squares
|
Degrees of
Freedom
|
Mean Sum
of Squares
|
F
|
|
Factor B
|
|
2
|
|
|
|
Factor A
|
600
|
|
200
|
|
|
Interaction
|
144
|
|
|
|
|
Error
|
384
|
12
|
|
|
|
Total
|
?1,288
|
23
|
|
|
What is the mean sum of squares for interaction of Factors A and B for this ANOVA? procedure?
- Consider the partially completed? one-way ANOVA summary table.
|
Source
|
Sum of Squares
|
Degrees of
Freedom
|
Mean Sum
of Squares
|
F
|
|
Between
|
270
|
|
|
|
|
Within
|
|
18
|
|
|
|
Total
|
810
|
21
|
|
|
What is the mean square within for this ANOVA? procedure?
- The test statistics for? one-way ANOVA follows the? _______.
- ?One-way ANOVA is used when we are looking at the influence that one factor has on the data values
- A software company would like to test if the standard deviation for the age of? "gamers" (those that routinely play video? games) is equal to 6.0 years. Which of the following would be the correct hypothesis? statement?
- Suppose Sony would like to test the hypothesis that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users. The following table summarizes sample statistics from each population.
| |
Playstation
|
Xbox
|
|
Sample standard deviation
|
4.3 years
|
3.9 years
|
|
Sample size
|
25
|
28
|
What is the correct hypothesis? statement?
- The? ________ measures how consistent the slope of the regression equation would be if several sets of samples from the population were selected and the regression equation were derived for each of them.
- Consider the partially completed randomized block ANOVA summary table.
|
Source
|
Sum of
Squares
|
Degrees of
Freedom
|
Mean Sum of
Squares
|
F
|
|
Between
|
600
|
3
|
|
|
|
Block
|
|
5
|
|
|
|
Error
|
750
|
|
|
|
|
Total
|
?2,150
|
23
|
|
|
What is the mean square between for this ANOVA? procedure?
- Consider the partially completed randomized block ANOVA summary table.
|
Source
|
Sum of
Squares
|
|
Degrees of
Freedom
|
Mean Sum of
Squares
|
F
|
|
Between
|
600
|
|
3
|
|
|
|
Block
|
|
|
5
|
|
|
|
Error
|
750
|
|
|
|
|
|
Total
|
?2,150
|
|
23
|
|
|
What is the blocking factor F-test statistic for this ANOVA? procedure?
