10-5. Exercises

1. BASIC

Ex 1. For the Basic and Application exercises in this section use the computations that were done for the exercises with the same number in Section 10.2 "The Linear Correlation Coefficient" and Section 10.4 "The Least Squares Regression Line".

Ex 2. Construct the 95% confidence interval for the slope $β_1$ of the population regression line based on the sample data set of Exercise 1 of Section 10.2 "The Linear Correlation Coefficient".

Ex 3. Construct the 90% confidence interval for the slope $β_1$ of the population regression line based on the sample data set of Exercise 2 of Section 10.2 "The Linear Correlation Coefficient".

Ex 4. Construct the 90% confidence interval for the slope $β_1$ of the population regression line based on the sample data set of Exercise 3 of Section 10.2 "The Linear Correlation Coefficient".

Ex 5. Construct the 99% confidence interval for the slope $β_1$ of the population regression Exercise 4 of Section 10.2 "The Linear Correlation Coefficient".

Ex 6. For the data in Exercise 5 of Section 10.2 "The Linear Correlation Coefficient" test, at the 10% level of significance, whether $x$ is useful for predicting $y$ (that is, whether $β_1≠0$ ).

Ex 7. For the data in Exercise 6 of Section 10.2 "The Linear Correlation Coefficient" test, at the 5% level of significance, whether $x$ is useful for predicting $y$ (that is, whether $β_1≠0$ ).

Ex 8. Construct the 90% confidence interval for the slope $β_1$ of the population regression line based on the sample data set of Exercise 7 of Section 10.2 "The Linear Correlation Coefficient".

Ex 9. Construct the 95% confidence interval for the slope $β_1$ of the population regression line based on the sample data set of Exercise 8 of Section 10.2 "The Linear Correlation Coefficient".

Ex 10. For the data in Exercise 9 of Section 10.2 "The Linear Correlation Coefficient" test, at the 1% level of significance, whether $x$ is useful for predicting $y$ (that is, whether $β_1≠0$ ).

Ex 11. For the data in Exercise 10 of Section 10.2 "The Linear Correlation Coefficient" test, at the 1% level of significance, whether $x$ is useful for predicting $y$ (that is, whether $β_1≠0$ ).

2. APPLICATIONS

Ex 12. For the data in Exercise 11 of Section 10.2 "The Linear Correlation Coefficient" construct a 90% confidence interval for the mean number of new words acquired per month by children between 13 and 18 months of age.

Ex 13. For the data in Exercise 12 of Section 10.2 "The Linear Correlation Coefficient" construct a 90% confidence interval for the mean increased braking distance for each additional 100 pounds of vehicle weight.

Ex 14. For the data in Exercise 13 of Section 10.2 "The Linear Correlation Coefficient" test, at the 10% level of significance, whether age is useful for predicting resting heart rate.

Ex 15. For the data in Exercise 14 of Section 10.2 "The Linear Correlation Coefficient" test, at the 10% level of significance, whether wind speed is useful for predicting wave height.

Ex 16. For the situation described in Exercise 15 of Section 10.2 "The Linear Correlation Coefficient"

1. Construct the 95% confidence interval for the mean increase in revenue per additional thousand dollars spent on advertising.

2. An advertising agency tells the business owner that for every additional thousand dollars spent on advertising, revenue will increase by over $25,000. Test this claim (which is the alternative hypothesis) at the 5% level of significance.

3. Perform the test of part (b) at the 10% level of significance.

4. Based on the results in (b) and (c), how believable is the ad agency’s claim? (This is a subjective judgement.)

Ex 17. For the situation described in Exercise 16 of Section 10.2 "The Linear Correlation Coefficient"

1. Construct the 90% confidence interval for the mean increase in height per additional inch of length at age two.

2. It is claimed that for girls each additional inch of length at age two means more than an additional inch of height at maturity. Test this claim (which is the alternative hypothesis) at the 10% level of significance.

Ex 18. For the data in Exercise 17 of Section 10.2 "The Linear Correlation Coefficient" test, at the 10% level of significance, whether course average before the final exam is useful for predicting the final exam grade.

Ex 19. For the situation described in Exercise 18 of Section 10.2 "The Linear Correlation Coefficient", an agronomist claims that each additional million acres planted results in more than 750,000 additional acres harvested. Test this claim at the 1% level of significance.

Ex 20. For the data in Exercise 19 of Section 10.2 "The Linear Correlation Coefficient" test, at the 1/10th of 1% level of significance, whether, ignoring all other facts such as age and body mass, the amount of the medication consumed is a useful predictor of blood concentration of the active ingredient.

Ex 21. For the data in Exercise 20 of Section 10.2 "The Linear Correlation Coefficient" test, at the 1% level of significance, whether for each additional inch of girth the age of the tree increases by at least two and one-half years.

Ex 22. For the data in Exercise 21 of Section 10.2 "The Linear Correlation Coefficient"

1. Construct the 95% confidence interval for the mean increase in strength at 28 days for each additional hundred psi increase in strength at 3 days.

2. Test, at the 1/10th of 1% level of significance, whether the 3-day strength is useful for predicting 28-day strength.

Ex 23. For the situation described in Exercise 22 of Section 10.2 "The Linear Correlation Coefficient"

1. Construct the 99% confidence interval for the mean decrease in energy demand for each one-degree drop in temperature.

2. An engineer with the power company believes that for each one-degree increase in temperature, daily energy demand will decrease by more than 3.6 million watt-hours. Test this claim at the 1% level of significance.

3. LARGE DATA SET EXERCISES

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Ex 24. Large Data Set 1 lists the SAT scores and GPAs of 1,000 students.

1. Compute the 90% confidence interval for the slope $β_1$ of the population regression line with SAT score as the independent variable ($x$) and GPA as the dependent variable ($y$).

2. Test, at the 10% level of significance, the hypothesis that the slope of the population regression line is greater than 0.001, against the null hypothesis that it is exactly 0.001.

Ex 25. Large Data Set 12 lists the golf scores on one round of golf for 75 golfers first using their own original clubs, then using clubs of a new, experimental design (after two months of familiarization with the new clubs).

1. Compute the 95% confidence interval for the slope $β_1$ of the population regression line with scores using the original clubs as the independent variable ($x$) and scores using the new clubs as the dependent variable ($y$).

2. Test, at the 10% level of significance, the hypothesis that the slope of the population regression line is different from 1, against the null hypothesis that it is exactly 1.

Ex 26. Large Data Set 13 records the number of bidders and sales price of a particular type of antique grandfather clock at 60 auctions.

1. Compute the 95% confidence interval for the slope $β_1$ of the population regression line with the number of bidders present at the auction as the independent variable ($x$) and sales price as the dependent variable ($y$).

2. Test, at the 10% level of significance, the hypothesis that the average sales price increases by more than $90 for each additional bidder at an auction, against the default that it increases by exactly $90.