In exercise 7, the data on y = annual sales ($1,000s) for new customer accounts and x = number of years of experience for a sample of 10 salespersons provided the estimated regression equation y = 80 + 4x. For these data x = 7, ∑(xi – x)2 = 142, and s = 4.6098.
a. Develop a 95% confidence interval for the mean annual sales for all salespersons with nine years of experience.
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.
c. Discuss the differences in your answers to parts (a) and (b).