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.
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.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 27PPS
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Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
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 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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