Many small restaurants in Portland, Oregon, and other cities across the United States do not take reservations. Owners say that with smaller capacity, no-shows are costly, and they would rather have their staff focused on customer service rather than maintaining a reservation system. However, it is important to be able to give reasonable estimates of waiting time when customers arrive and put their names on the waiting list. The file RestaurantLine contains 10 observations of number of people in line ahead of a customer (independent variable x) and actual waiting time (dependent variable y). The estimated regression equation is: ŷ=7.82+8.84x and MSE=113.9197. Point estimate for customers with 3 people on the waitlist is 34.3 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). 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).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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Many small restaurants in Portland, Oregon, and other cities across the United States do not take reservations. Owners say that with smaller capacity, no-shows are costly, and they would rather have their staff focused on customer service rather than maintaining a reservation system. However, it is important to be able to give reasonable estimates of waiting time when customers arrive and put their names on the waiting list. The file RestaurantLine contains 10 observations of number of people in line ahead of a customer (independent variable x) and actual waiting time (dependent variable y). The estimated regression equation is: ŷ=7.82+8.84x and MSE=113.9197. Point estimate for customers with 3 people on the waitlist is 34.3 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).

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 Number of Customers [Waiting Time (Minutes)
2
4
58
3
3
38
4
37
5
45
6
7
73
7
42
8
8
83
9
4
54
10
7
70
11
4
29
4-
Transcribed Image Text:1 Number of Customers [Waiting Time (Minutes) 2 4 58 3 3 38 4 37 5 45 6 7 73 7 42 8 8 83 9 4 54 10 7 70 11 4 29 4-
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