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 µ, in this exercise we wish to investigate whether the sample of 99 waiting times provides evidence to support the claim that µ is less than 6. For the sake of argument, we will begin by assuming that µ equals 6, and we will then attempt to use the sample to contradict this assumption in favor of the conclusion that u is less than 6. Recall that the mean of the sample of 99 waiting times is i = 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 ? Normal because the sample is large
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 µ, in this exercise we wish to investigate whether the sample of 99 waiting times provides evidence to support the claim that µ is less than 6. For the sake of argument, we will begin by assuming that µ equals 6, and we will then attempt to use the sample to contradict this assumption in favor of the conclusion that u is less than 6. Recall that the mean of the sample of 99 waiting times is i = 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 ? Normal because the sample is large
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
![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 H, in this
exercise we wish to investigate whether the sample of 99 waiting times provides evidence to support the claim that u 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 u is less than 6. Recall that the mean of the sample of 99 waiting times is i = 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 ?
Normal because the sample is
large](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe25867c-b393-4b1b-8545-ed6d3cde7ea9%2F65e8d814-7d09-4320-8b45-a21438c35981%2Fr8j5fls_processed.png&w=3840&q=75)
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 H, in this
exercise we wish to investigate whether the sample of 99 waiting times provides evidence to support the claim that u 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 u is less than 6. Recall that the mean of the sample of 99 waiting times is i = 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 ?
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.)
uX = 6, ox =
(c) The sample mean that we have actually observed is i = 5.39. Assuming that u equals 6, find the probability of observing a sample
mean that is less than or equal to x = 5.39. (Round "z-value" to 2 decimals and final answer to 4 decimal places.)
P(x < 5.39)
(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 u is
than 6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe25867c-b393-4b1b-8545-ed6d3cde7ea9%2F65e8d814-7d09-4320-8b45-a21438c35981%2Fv9jkk8hp_processed.png&w=3840&q=75)
Transcribed Image Text:(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.)
uX = 6, ox =
(c) The sample mean that we have actually observed is i = 5.39. Assuming that u equals 6, find the probability of observing a sample
mean that is less than or equal to x = 5.39. (Round "z-value" to 2 decimals and final answer to 4 decimal places.)
P(x < 5.39)
(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 u is
than 6.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
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](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
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](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman