Chapter 14.6, Problem 36E

In exercise 7, the data on y = annual sales ($ 1000s) for new customer accounts and x = number of years of experience for a sample of 10 salespersons provided the estimated regression equation ŷ = 80 + 4x. For these data $\bar{x}=7,\sum {\left(x_i-\bar{x}\right)}^2=142$, and s = 4.6098.

1. a. Develop a 95% confidence interval for the mean annual sales for all salespersons with nine years of experience.
2. b. The company is considering hiring Tom Smart, a salesperson with nine years of experience. Develop a 95% prediction interval of annual sales for Tom Smart.
3. c. Discuss the differences in your answers to parts (a) and (b).