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".

1. 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".

3. 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".

5. 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 $β_1≠0$ ).

7. 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".

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 $y$ (that is, whether $β_1≠0$).

#### 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"

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