Homework answers / question archive / Section 10

Section 10

Statistics

Share With

---

Section 10.3 Homework

Choose the correct answer below.

A. The first equation is for sample data; the second equation is for a population.

B. The first equation is for a population; the second equation is for sample data.

2. Suppose IQ scores were obtained from randomly selected siblings. For 20 such pairs of people, the linear correlation coefficient is 0.907 and the equation of the regression line is y = 9.09 + 0.93x, where x represents the IQ score of the older child. Also, the 20 x values have a mean of 104.51 and the 20 y values have a mean of 106.65. What is the best predicted IQ of the younger child, given that the older child has an IQ of 103? Use a significance level of 0.05.

1 Click the icon to view the critical values of the Pearson correlation coefficient r.

 

(Round to two decimal places as needed.)

Critical Values of the Pearson Correlation Coefficient r

n             α = 0.05                α = 0.01

4              0.950     0.990

5              0.878     0.959

6              0.811     0.917

7              0.754     0.875

8              0.707     0.834

9              0.666     0.798

10           0.632     0.765

11           0.602     0.735

12           0.576     0.708

13           0.553     0.684

14           0.532     0.661

15           0.514     0.641

16           0.497     0.623

17           0.482     0.606

18           0.468     0.590

19           0.456     0.575

20           0.444     0.561

25           0.396     0.505

30           0.361     0.463

35           0.335     0.430

40           0.312     0.402

45           0.294     0.378

50           0.279     0.361

60           0.254     0.330

70           0.236     0.305

80           0.220     0.286

90           0.207     0.269

100         0.196     0.256

n             α = 0.05                α = 0.01

1: Critical Values of the Pearson Correlation Coefficient r

 

NOTE: To test H0: ρ = 0 against H1: ρ≠ 0, reject H0 if the absolute value of r is greater than the critical value in the table.

Section 10.3 Homewo

3.            A sample of 100 women is obtained, and their heights (in inches) and pulse rates (in beats per minute) are measured. The

 

linear correlation coefficient is 0.219 and the equation of the regression line is y = 18.2 + 0.940x, where x represents height. The mean of the 100 heights is 63.4 in and the mean of the 100 pulse rates is 75.1 beats per minute. Find the best predicted pulse rate of a woman who is 74 in tall. Use a significance level of α = 0.01. 2 Click the icon to view the critical values of the Pearson correlation coefficient r.

The best predicted pulse rate of a woman who is 74 in tall is        beats per minute.

(Type an integer or decimal rounded to two decimal places as needed.)

Critical Values of the Pearson Correlation Coefficient r

n             α = 0.05                α = 0.01

4              0.950     0.990

5              0.878     0.959

6              0.811     0.917

7              0.754     0.875

8              0.707     0.834

9              0.666     0.798

10           0.632     0.765

11           0.602     0.735

12           0.576     0.708

13           0.553     0.684

14           0.532     0.661

15           0.514     0.641

16           0.497     0.623

17           0.482     0.606

18           0.468     0.590

19           0.456     0.575

20           0.444     0.561

25           0.396     0.505

30           0.361     0.463

35           0.335     0.430

40           0.312     0.402

45           0.294     0.378

50           0.279     0.361

60           0.254     0.330

70           0.236     0.305

80           0.220     0.286

90           0.207     0.269

100         0.196     0.256

n             α = 0.05                α = 0.01

2: Critical Values of the Pearson Correlation Coefficient r

 

NOTE: To test H0: ρ = 0 against H1: ρ≠ 0, reject H0

if the absolute value of r is greater than the critical value in the table.

 

Section 10.3 Homework-

4.            Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.

 

x              12           5              8              7              11           14           4              10           6              9              13

y              7.77        3.81        7.48        6.59        8.19        5.93        1.93        8.28        5.37        8.05        7.01

Create a scatterplot of the data. Choose the correct graph below.

 A.           B.           C.           D.

Identify a characteristic of the data that is ignored by the regression line.

b.            What is the equation of the regression line for the set of 9 points?

  (Round to three decimal places as needed.)

c.             Choose the correct description of the results below.

Section 10.3 Homework

6.            The data show the time intervals after an eruption (to the next eruption) of a certain geyser. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted time of the interval after an eruption given

What is the best predicted time for the interval after an eruption that is 136 feet high?

The best predicted interval time for an eruption that is 136 feet high is   minutes.

(Round to one decimal place as needed.)

Critical Values of the Pearson Correlation Coefficient r

n             α = 0.05                α = 0.01

4              0.950     0.990

5              0.878     0.959

6              0.811     0.917

7              0.754     0.875

8              0.707     0.834

9              0.666     0.798

10           0.632     0.765

11           0.602     0.735

12           0.576     0.708

13           0.553     0.684

14           0.532     0.661

15           0.514     0.641

16           0.497     0.623

17           0.482     0.606

18           0.468     0.590

19           0.456     0.575

20           0.444     0.561

25           0.396     0.505

30           0.361     0.463

35           0.335     0.430

40           0.312     0.402

45           0.294     0.378

50           0.279     0.361

60           0.254     0.330

70           0.236     0.305

80           0.220     0.286

90           0.207     0.269

100         0.196     0.256

3: Critical Values of the Pearson Correlation Coefficient r

NOTE: To test H0: ρ = 0 against H1: ρ≠ 0, reject H0

if the absolute value of r is greater than the critical value in the table.

Section 10.3 Homework-

7.            The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the systolic reading be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 118. Is the predicted value close to 77.3, which was the actual diastolic reading? Use a significance level of 0.05.

Systolic 150         124         149         120         114

                135         136         116

Diastolic               109                                                                                                        

4              Click the icon to view the critical values of the Pearson correlation coefficient r.

What is the best predicted diastolic pressure for a person with a systolic reading of 118?

The best predicted diastolic pressure for a person with a systolic reading of 118 is  . (Round to one decimal place as needed.)

Is the predicted value close to 77.3, which was the actual diastolic reading?

A.            The predicted value is very close to the actual diastolic reading.

B.            The predicted value is exactly the same as the actual diastolic reading.

C.            The predicted value is not close to the actual diastolic reading.

D.            The predicted value is close to the actual diastolic reading.

4: Critical Values of the Pearson Correlation Coefficient r

 

Section 10.3 Homewo  

NOTE: To test H0: ρ = 0 against H1: ρ≠ 0, reject H0

Critical Values of the Pearson Correlation Coefficient r

n             α = 0.05                α = 0.01

4              0.950     0.990

5              0.878     0.959

6              0.811     0.917

7              0.754     0.875

8              0.707     0.834

9              0.666     0.798

10           0.632     0.765

11           0.602     0.735

12           0.576     0.708

13           0.553     0.684

14           0.532     0.661

15           0.514     0.641

16           0.497     0.623

17           0.482     0.606

18           0.468     0.590

19           0.456     0.575

20           0.444     0.561

25           0.396     0.505

30           0.361     0.463

35           0.335     0.430

40           0.312     0.402

45           0.294     0.378

50           0.279     0.361

60           0.254     0.330

70           0.236     0.305

80           0.220     0.286

90           0.207     0.269

100         0.196     0.256

n             α = 0.05                α = 0.01

if the absolute value of r is greater than the critical value in the table.

Section 10.3 Homework

8.            The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 40 inches. Is the result close to the actual weight of 272 pounds? Use a significance level of 0.05.

Chest size (inches)          41           54           44           55

                39           51

Weight (pounds)              328                                                                        

5              Click the icon to view the critical values of the Pearson correlation coefficient r.

What is the best predicted weight of a bear with a chest size of 40 inches?

The best predicted weight for a bear with a chest size of 40 inches is    pounds. (Round to one decimal place as needed.)

Is the result close to the actual weight of 272 pounds?

A.            This result is exactly the same as the actual weight of the bear.

B.            This result is not very close to the actual weight of the bear.

C.            This result is very close to the actual weight of the bear.

D.            This result is close to the actual weight of the bear.

5: Critical Values of the Pearson Correlation Coefficient r

  

Section 10.3 Homew

n             α = 0.05                α = 0.01

4              0.950     0.990

5              0.878     0.959

6              0.811     0.917

7              0.754     0.875

8              0.707     0.834

9              0.666     0.798

10           0.632     0.765

11           0.602     0.735

12           0.576     0.708

13           0.553     0.684

14           0.532     0.661

15           0.514     0.641

16           0.497     0.623

17           0.482     0.606

18           0.468     0.590

19           0.456     0.575

20           0.444     0.561

25           0.396     0.505

30           0.361     0.463

35           0.335     0.430

40           0.312     0.402

45           0.294     0.378

50           0.279     0.361

60           0.254     0.330

70           0.236     0.305

80           0.220     0.286

90           0.207     0.269

100         0.196     0.256

n             α = 0.05                α = 0.01

Critical Values of the Pearson Correlation Coefficient r

NOTE: To test H0: ρ = 0 against H1: ρ≠ 0, reject H0

if the absolute value of r is greater than the critical value in the table.

Section 10.3 Homew

9.            Find the regression equation, letting overhead width be the predictor (x) variable. Find the best predicted weight of a seal if the overhead width measured from a photograph is 2 cm. Can the prediction be correct? What is wrong with predicting the weight in this case? Use a significance level of 0.05.

Overhead Width (cm)    8.2          7.9          8.8          8.3          9.9          7.2

Weight (kg)        187         204         239         190         283         170

Can the prediction be correct? What is wrong with predicting the weight in this case?

A.            The prediction cannot be correct because a negative weight does not make sense. The width in this case is beyond the scope of the available sample data.

B.            The prediction cannot be correct because there is not sufficient evidence of a linear correlation. The width in this case is beyond the scope of the available sample data.

C.            The prediction cannot be correct because a negative weight does not make sense and because

D.            The prediction can be correct. There is nothing wrong with predicting the weight in this case.

6: Critical Values of the Pearson Correlation Coefficient r

  

 

Section 10.3 Homewo

n             α = 0.05                α = 0.01

4              0.950     0.990

5              0.878     0.959

6              0.811     0.917

7              0.754     0.875

8              0.707     0.834

9              0.666     0.798

10           0.632     0.765

11           0.602     0.735

12           0.576     0.708

13           0.553     0.684

14           0.532     0.661

15           0.514     0.641

16           0.497     0.623

17           0.482     0.606

18           0.468     0.590

19           0.456     0.575

20           0.444     0.561

25           0.396     0.505

30           0.361     0.463

35           0.335     0.430

40           0.312     0.402

45           0.294     0.378

50           0.279     0.361

60           0.254     0.330

70           0.236     0.305

80           0.220     0.286

90           0.207     0.269

100         0.196     0.256

n             α = 0.05                α = 0.01

Critical Values of the Pearson Correlation Coefficient r

NOTE: To test H0: ρ = 0 against H1: ρ≠ 0, reject H0

if the absolute value of r is greater than the critical value in the table.

Section 10.3 Homewo    https://xlitemprod.pearsoncmg.com/api/v1/print/math

10.          The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000

 

What is the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute?

The best predicted temperature when a bug is chirping at 3000 chirps per minute is  °F.

(Round to one decimal place as needed.)

What is wrong with this predicted value? Choose the correct answer below.

A.            The first variable should have been the dependent variable.

B.            It is unrealistically high. The value 3000 is far outside of the range of observed values.

C.            It is only an approximation. An unrounded value would be considered accurate.

D.            Nothing is wrong with this value. It can be treated as an accurate prediction. 

                 https://xlitemprod.pearsoncmg.com/api/v1/print/math

11.          Find the regression equation, letting the diameter be the predictor (x) variable. Find the best predicted circumference of a marble with a diameter of 1.5 cm. How does the result compare to the actual circumference of 4.7 cm? Use a significance level of 0.05.

                Baseball               Basketball           Golf       Soccer   Tennis   Ping-Pong           Volleyball

Diameter             7.3          24.3        4.3          22.2        6.9          3.9          21.4

Circumference  22.9        76.3        13.5        69.7        21.7        12.3        67.2

 

How does the result compare to the actual circumference of 4.7 cm?

A.            Since 1.5 cm is beyond the scope of the sample diameters, the predicted value yields a very different circumference.

B.            Even though 1.5 cm is within the scope of the sample diameters, the predicted value yields a very different circumference.

C.            Since 1.5 cm is within the scope of the sample diameters, the predicted value yields the actual circumference.

D.            Even though 1.5 cm is beyond the scope of the sample diameters, the predicted value yields the actual circumference.

7: Critical Values of the Pearson Correlation Coefficient r

  

 

 

n             α = 0.05                α = 0.01

4              0.950     0.990

5              0.878     0.959

6              0.811     0.917

7              0.754     0.875

8              0.707     0.834

9              0.666     0.798

10           0.632     0.765

11           0.602     0.735

12           0.576     0.708

13           0.553     0.684

14           0.532     0.661

15           0.514     0.641

16           0.497     0.623

17           0.482     0.606

18           0.468     0.590

19           0.456     0.575

20           0.444     0.561

25           0.396     0.505

30           0.361     0.463

35           0.335     0.430

40           0.312     0.402

45           0.294     0.378

50           0.279     0.361

60           0.254     0.330

70           0.236     0.305

80           0.220     0.286

90           0.207     0.269

100         0.196     0.256

n             α = 0.05                α = 0.01

Critical Values of the Pearson Correlation Coefficient r

NOTE: To test H0: ρ = 0 against H1: ρ≠ 0, reject H0 if the absolute value of r is greater than the critical value in the table.

 

                 https://xlitemprod.pearsoncmg.com/api/v1/print/math

12.          Use the data consisting of IQ score and brain volume (cm3). Find the best predicted IQ score for someone with a brain

volume of 1003 cm3. Use a significance level of 0.05.

8 Click the icon to view the data set.

Click here to view the critical values of the Pearson correlation coefficient, r.9

The regression equation is y =    +             x.

(Round the x-coefficient to five decimal places as needed. Round the constant to two decimal places as needed.)

Given a brain volume of 1003 cm3, the best predicted IQ score is              .

(Round to the nearest integer as needed.)

8:  Brain Volume vs. IQ Score

 

Brain Volume     IQ score              

1030       127

1265       107

900         84

1336       98

1095       92

1167       127

963         113

1459       124

1391       120 1380               99

930         106

962         105

1035       86

912         128

1158       117

1375       96

1276       91

1017       94

1250       101

1058       129

9: Critical Values of the Pearson Correlation Coefficient r

 

Section 10.3 Homewo

Critical Values of the Pearson Correlation Coefficient r

n             α = 0.05                α = 0.01

4              0.950     0.990

5              0.878     0.959

6              0.811     0.917

7              0.754     0.875

8              0.707     0.834

9              0.666     0.798

10           0.632     0.765

11           0.602     0.735

12           0.576     0.708

13           0.553     0.684

14           0.532     0.661

15           0.514     0.641

16           0.497     0.623

17           0.482     0.606

18           0.468     0.590

19           0.456     0.575

20           0.444     0.561

25           0.396     0.505

30           0.361     0.463

35           0.335     0.430

40           0.312     0.402

45           0.294     0.378

50           0.279     0.361

60           0.254     0.330

70           0.236     0.305

80           0.220     0.286

90           0.207     0.269

100         0.196     0.256

n             α = 0.05                α = 0.01

NOTE: To test H0: ρ = 0 against H1: ρ≠ 0, reject H0 if the absolute value of r is greater than the critical value in the table.

 

 

Section 10.3 Homework

13.          Fifty matched pairs of magnitude/depth measurements randomly selected from 10,594 earthquakes recorded in one year from a location in southern California. Find the best predicted depth of an earthquake with a magnitude of 2.2. Use a significance level of 0.05.

10 Click the icon to view the earthquake measurements.

Click here to view the critical values of the Pearson correlation coefficient, r.11

 

(Round to one decimal place as needed.)

Given that the earthquake has a magnitude of 2.2, the best predicted depth is    km. (Round to one decimal place as needed.)

10:  Earthquake Measurements

  

Section 10.3 Homework

Mag       Depth  

1.01        10.3

1.62        5.1

1.04        7.6

0.41        11.9

1.22        11.1

0.79        13.8

0.78        8.3

1.93        17.2

1.39        9.6

0.82        11.9

0.07        9.8

1.23        19.8

0.46        14.8

2.14        11.5

1.43        14.3

0.27        6.1

2.88        11.2

0.57        6.7

1.58        2.7

1.91        9.3

2.65        5.7

2.47        7.3

2.57        10.6

2.28        14.8

1.82        19.3

0.88        2.6

1.85        6.2

2.55        4.5

1.25        12.1

2.92        10.5

2.13        16.5

2.17        6.7

1.68        12.7

0.83        6.5

2.89        10.2

0.05        8.5

1.72        15.5

1.79        8.7

1.44        5.9

2.29        4.2

2.31        17.1

1.68        18.4

Section 10.3 Homew

1.48        6.3

2.57        17.5

1.51        3.1

2.71        19.4

11: Critical Values of the Pearson Correlation Coefficient r

 

n             α = 0.05                α = 0.01

4              0.950     0.990

5              0.878     0.959

6              0.811     0.917

7              0.754     0.875

8              0.707     0.834

9              0.666     0.798

10           0.632     0.765

11           0.602     0.735

12           0.576     0.708

13           0.553     0.684

14           0.532     0.661

15           0.514     0.641

16           0.497     0.623

17           0.482     0.606

18           0.468     0.590

19           0.456     0.575

20           0.444     0.561

25           0.396     0.505

30           0.361     0.463

35           0.335     0.430

40           0.312     0.402

45           0.294     0.378

50           0.279     0.361

60           0.254     0.330

70           0.236     0.305

80           0.220     0.286

90           0.207     0.269

100         0.196     0.256

n             α = 0.05                α = 0.01

Critical Values of the Pearson Correlation Coefficient r

NOTE: To test H0: ρ = 0 against H1: ρ≠ 0, reject H0

if the absolute value of r is greater than the critical value in the table.

 

Section 10.3 Homew

14.          Which of the following is not a requirement for regression analysis?

 

Choose the correct answer below.

 

 

Given a collection of paired sample data, the ____________________ y = b0 + b1x algebraically describes the relationship between the two variables, x and y.

 0             1 between the two variables, x and y.

 

 

 

Choose the correct answer below.

A.            If the regression equation does not appear to be useful for making predictions, the best predicted value of a variable is its point estimate.

B.            Use the regression equation for predictions only if the linear correlation coefficient r indicates that there is a linear correlation between the two variables.

C.            Use the regression equation for predictions only if the graph of the regression line on the scatterplot confirms that the regression line fits the points reasonably well.

D.            Use the regression line for predictions only if the data go far beyond the scope of the available sample data.

Section 10.3 Homework

18.          Fill in the blank.

In working with two variables related by a regression equation, the _________________ in a variable is the amount that it changes when the other variable changes by exactly one unit.

In working with two variables related by a regression equation, the (1) in a variable is the amount that it changes when the other variable changes by exactly one unit.

 

In a scatterplot, a(n) ______________ is a point lying far away from the other data points.

 

 

Paired sample data may include one or more ___________, which are points that strongly affect the graph of the regression line.

Paired sample data may include one or more (1)               which are points that strongly affect the graph of the regression line.

 

For a pair of sample x- and y-values, the ______________ is the difference between the observed sample value of y and the y-value that is predicted by using the regression equation.

For a pair of sample x- and y-values, the (1)         is the difference between the observed sample value of y and the y-value that is predicted by using the regression equation.

 

 

Section 10.3 Homew

22.          Fill in the blank.

A straight line satisfies the __________________ if the sum of the squares of the residuals is the smallest sum possible.

A straight line satisfies the (1)    if the sum of the squares of the residuals is the smallest sum possible.