The bank manager wants to show that the new system reduces typical customer waiting times to less than 6 minutes. One way to do this is to demonstrate that the mean of the population of all customer waiting times is less than 6. Letting this mean be u, in this exercise we wish to investigate whether the sample of 99 waiting times. provides evidence to support the claim that is less than 6. equals 6, and we will For the sake of argument, we will begin by assuming that then attempt to use the sample to contradict this assumption in favor of the conclusion that is less than 6. Recall that the mean of the sample of 99 waiting times is x = 5.39 and assume that a, the standard deviation of the population of all customer waiting times, is known to be 2.22. (a) Consider the population of all possible sample means obtained from random samples of 99 waiting times. What is the shape of this population of sample means? That is, what is the shape of the sampling distribution of x? Normal because the sample is large (b) Find the mean and standard deviation of the population of all possible sample means when we assume that u equals 6. (Round your answer to 4 decimal places.) H₁=6,0₁=( (c) The sample mean that we have actually observed is x = 5.39. Assuming that u equals 6, find the probability of observing a sample mean that is less than or equal to 5.39. (Round your answer to 4 decimal places.) (d) If u equals 6, what percentage of all possible sample means are less than or equ to 5.39? What do you conclude about whether the new system has reduced the typical customer waiting time to less than 6 minutes? (Round your answer to 2 decimal places.) %; conclude that is (less than 6.
The bank manager wants to show that the new system reduces typical customer waiting times to less than 6 minutes. One way to do this is to demonstrate that the mean of the population of all customer waiting times is less than 6. Letting this mean be u, in this exercise we wish to investigate whether the sample of 99 waiting times. provides evidence to support the claim that is less than 6. equals 6, and we will For the sake of argument, we will begin by assuming that then attempt to use the sample to contradict this assumption in favor of the conclusion that is less than 6. Recall that the mean of the sample of 99 waiting times is x = 5.39 and assume that a, the standard deviation of the population of all customer waiting times, is known to be 2.22. (a) Consider the population of all possible sample means obtained from random samples of 99 waiting times. What is the shape of this population of sample means? That is, what is the shape of the sampling distribution of x? Normal because the sample is large (b) Find the mean and standard deviation of the population of all possible sample means when we assume that u equals 6. (Round your answer to 4 decimal places.) H₁=6,0₁=( (c) The sample mean that we have actually observed is x = 5.39. Assuming that u equals 6, find the probability of observing a sample mean that is less than or equal to 5.39. (Round your answer to 4 decimal places.) (d) If u equals 6, what percentage of all possible sample means are less than or equ to 5.39? What do you conclude about whether the new system has reduced the typical customer waiting time to less than 6 minutes? (Round your answer to 2 decimal places.) %; conclude that is (less than 6.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Sp
Subject: statistics
Transcribed Image Text:The bank manager wants to show that the new system reduces typical customer
waiting times to less than 6 minutes. One way to do this is to demonstrate that the
mean of the population of all customer waiting times is less than 6. Letting this mean
be , in this exercise we wish to investigate whether the sample of 99 waiting times
provides evidence to support the claim that is less than 6.
For the sake of argument, we will begin by assuming that u equals 6, and we will
then attempt to use the sample to contradict this assumption in favor of the conclusion
that is less than 6. Recall that the mean of the sample of 99 waiting times is x = 5.39
and assume that o, the standard deviation of the population of all customer waiting
times, is known to be 2.22.
(a) Consider the population of all possible sample means obtained from random
samples of 99 waiting times. What is the shape of this population of sample means?
That is, what is the shape of the sampling distribution of x?
Normal because the sample is large
(b) Find the mean and standard deviation of the population of all possible sample
means when we assume that equals 6. (Round your answer to 4 decimal places.)
H₁=6,0₁ =
(c) The sample mean that we have actually observed is x = 5.39. Assuming that u
equals 6, find the probability of observing a sample mean that is less than or equal
to 5.39. (Round your answer to 4 decimal places.)
(d) If u equals 6, what percentage of all possible sample means are less than or equal
to 5.39? What do you conclude about whether the new system has reduced the
typical customer waiting time to less than 6 minutes? (Round your answer to 2
decimal places.)
%; conclude that is less
than 6.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 12 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman