Many small restaurants in Portland, Oregon, and other cities across the United States do not take reservations. Owners s
Posted: Wed May 11, 2022 7:40 pm
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 ---Select--- wider narrower than the
confidence interval. This is because it
is ---Select--- more less 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.
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 ---Select--- wider narrower than the
confidence interval. This is because it
is ---Select--- more less 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.