Question

Number of Customers	Waiting Time (Minutes)
5	47
2	27
4	36
4	44
6	52
3	21
7	82
3	43
8	69
4	28

You may need to use the appropriate appendix table or technology to answer this question.

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 four 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 four 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 four 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  ---Select--- wider narrower than the confidence interval. This is because it is  ---Select--- less more difficult to predict the waiting time for an individual customer arriving with four people in line than it is to estimate the mean waiting time for a customer arriving with four people in line.

Answer 1