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 name 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 (in minutes) (dependent variable y). The estimated regression equation is: ŷ = 4.35 + 8.81x and MSE = 94.42. (a) Develop a point estimate (in min) for a customer who arrives with seven people on the wait-list. (Round your answer to two decimal places.) ŷ* = ___min (b) Develop a 95% confidence interval for the mean waiting time (in min) for a customer who arrives with seven customers already in line. (Round your answers to two decimal places.) _min to __ min (c) Develop a 95% prediction interval for Roger and Sherry Davy's waiting time (in min) if there are seven customers in line when they arrive. (Round your answers to two decimal places.) _min to __ min (d) Discuss the difference between part (b) and part (c). The prediction interval is much { wider/ narrower }than the confidence interval. This is because it is {less /more} difficult to predict the waiting time for an individual customer arriving with seven people in line than it is to estimate the mean waiting time for a customer arriving with seven people in line.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 name 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 (in minutes) (dependent variable y). The estimated regression equation is:

ŷ = 4.35 + 8.81x and MSE = 94.42.

(a) Develop a point estimate (in min) for a customer who arrives with seven people on the wait-list. (Round your answer to two decimal places.)

ŷ^* = _____min

(b) Develop a 95% confidence interval for the mean waiting time (in min) for a customer who arrives with seven customers already in line. (Round your answers to two decimal places.)

_____min to ______ min

(c) Develop a 95% prediction interval for Roger and Sherry Davy's waiting time (in min) if there are seven customers in line when they arrive. (Round your answers to two decimal places.)

_____min to ____ min

(d) Discuss the difference between part (b) and part (c).

The prediction interval is much { wider/ narrower }than the confidence interval. This is because it is {less /more} difficult to predict the waiting time for an individual customer arriving with seven people in line than it is to estimate the mean waiting time for a customer arriving with seven people in line.

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