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4.

Many small restaurants in Portland, Oregon, and other cities across the United States do not take reservations. Owners say that with smaller capacity, noshows are costly, and they would rather have their staff focused on customer service rather than maintaining a reservation system (pressherald.com). However, it is important to be able to give reasonable estimates of waiting time when customers arrive and put their name on the waiting list. The file RestaurantLine contains 10 observations of number of people in line ahead of a customer (independent variable :19) and actual waiting time (dependent variable y). The estimated regression equation is: :17 = 0.30 + 8.3250 and MSE = 80.1952. Click on the datafile logo to reference the data. DATAr Use Table 2 of Appendix B. 3. Develop a point estimate for a customer who arrive with three people on the wait-list (to 1 decimal). 25.26 0 minutes b. Develop a 95% confidence interval for the mean waiting time for a customer who arrives with three customers already in line (to 2 decimals). ( 13.73 0minutes, 36.67 ominutes) c. Develop a 95% prediction interval for Roger and Sherry Davy's waiting time if there are three customers in line when they arrive (to 2 decimals). ( 1.58 0minutes, 48.52 0minutes) d. Discuss the differences in your answers to parts (b) and (c). The prediction interval is Q9 than the condence interval. \fA sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons. Years of Annual Sales Salesperson Experience ($10005) 1 1 80 2 3 96 3 5 98 4 7 98 5 9 104 6 11 122 7 12 132 8 13 150 9 14 152 10 14 170 The data on y = annual sales ($10003) for new customer accounts and a: = number of years of experience for a sample of 10 salespersons provided the estimated regression equation Q = 68.02 + 5.8633. For these data 5 = 8.9, 2(1, if = 198.90, and s = 11.9053. a. Develop the 95% confidence interval for the mean annual sales ($10006) for all salespersons with eight years of experience. ($ 95.73 0, $ 63.75 0) (t02 decimals) b. The company is considering hiring Tom Smart, a salesperson with eight years of experience. Develop a 95% prediction interval of annual sales ($10008) for Tom Smart. ($ 111.52 0, $ 47.97 0) (to 2 decimals) c. Discuss the differences in your answers to parts (a) and (b). As expected, the prediction interval is much \\'0 than the confidence interval. This is due to the fact that it is more K20 to predict annual sales for one new salesperson with 8 years of experience than it is to estimate the mean annual sales for all salespersons with 8 years of experience