## Statistical Inference about Slope

This section further details two types of inferences on the slope parameter, considering both confidence intervals and hypothesis testing.

### Exercises

#### Basic

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".

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

5. For the data in Exercise 5 of Section 10.2 "The Linear Correlation Coefficient" test, at the 10% level of significance, whether is useful for predicting (that is, whether ).

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

9. 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 (that is, whether ).

#### Applications

11. 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.

13. 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.

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

- Construct the 95% confidence interval for the mean increase in revenue per additional thousand dollars spent on advertising.
- 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.
- Perform the test of part (b) at the 10% level of significance.
- Based on the results in (b) and (c), how believable is the ad agency’s claim? (This is a subjective judgement.)

17. 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.

19. 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.

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

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

#### Large Data Set Exercises

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

http://www.gone.2012books.lardbucket.org/sites/all/files/data1.xls

- Compute the 90% confidence interval for the slope of the population regression line with SAT score as the independent variable and GPA as the dependent variable .
- 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.

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

http://www.gone.2012books.lardbucket.org/sites/all/files/data13.xls

- Compute the 95% confidence interval for the slope of the population regression line with the number of bidders present at the auction as the independent variable and sales price as the dependent variable .
- 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.