Exercises. 1. Construct a 99% confidence interval for the mean value of y and a 99% prediction interval for the predicted value of y for the following

1. Construct a 99% confidence interval for the mean value of y and a 99% prediction interval for the predicted value of y for the following

a) for given ;

; ; and

b) for given ; ;

; and

2. Refer to Exercise 4 of the previous section. Construct a 90% confidence interval for the mean monthly salary of secretaries with 10 years of experience. Construct a 90% prediction interval for the monthly salary of a randomly selected secretary with 10 years of experience.

3. Refer to Exercise 6 of the previous section. Construct a 95% confidence interval for the mean number of breakdowns for all cars which are 16 years old. Determine a 95% prediction interval for for .

4. The following data give information on the lowest cost price (in dollars) and the average attendance (thousand) for the past year for eight football teams

Ticket price	3.6	3.3	2.8	2.6	2.7	2.9	2.0	2.6
Attendance

a) Taking ticket price as an independent variable and attendance as a dependent variable, estimate the regression of attendance on the ticket price.

b) Interpret the slope of the estimated regression line.

c) Find and interpret the coefficient of determination.

d) Find and interpret a 90% confidence interval for the slope of the population regression line.

e) Find a 90% confidence interval for expected number of attendance for which the price of ticket is 20.

5. A sample of 25 employees at a production plant was taken. Each employee was asked to assess his or her own job satisfaction (x), on scale from 1 to 10. In addition, the number of days absent (y) from work during the last year were found for these employees. The sample regression line

was estimated by least squares for these data. Also found that

; ;

a) Test at the 1% significance level against the appropriate one sided alternative the null hypothesis that job satisfaction has no linear effect on absence.

b) A particular employee has job satisfaction level 4. Find a 90% confidence interval for the number of days this employee would be absent from work in a year.

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