You are a bank manager and you want to secure a raise for your bank tellers. The board of trustees show financial data indicating that 15 customers a day is the average number of clients served for bank tellers in your region. If you can provide convincing evidence that your bank tellers are actually serving a greater number of clients per day, they will grant a 10% raise. Over the next week, you measure the average number of customers served by the 31 bank tellers at your local branch and determine that their average is 20 customers a day with a standard deviation of 3. Do you have sufficient evidence to argue for a raise? you a. Write out the null and alternative/research hypothesis b. Using the .05 level of significance, find the critical value(s) and sketch the comparison distribution with rejection region(s) shaded in c. Calculate the value of the test statistic that you will then compare to your critical value(s) d. State your decision based on the results e. Write a conclusion statement that clearly expresses what your decision means f. What is the probability that you have committed a Type 1 error? g. How could you change your approach to this hypothesis test to decrease the chances of making a Type 1 error? (Hint: Focus on step b) h. Does decreasing the chances of making a Type 1 error make it easier or harder to reject the Null Hypothesis? What evidence are you using to make your decision?
You are a bank manager and you want to secure a raise for your bank tellers. The board of trustees show financial data indicating that 15 customers a day is the average number of clients served for bank tellers in your region. If you can provide convincing evidence that your bank tellers are actually serving a greater number of clients per day, they will grant a 10% raise. Over the next week, you measure the average number of customers served by the 31 bank tellers at your local branch and determine that their average is 20 customers a day with a standard deviation of 3. Do you have sufficient evidence to argue for a raise? you a. Write out the null and alternative/research hypothesis b. Using the .05 level of significance, find the critical value(s) and sketch the comparison distribution with rejection region(s) shaded in c. Calculate the value of the test statistic that you will then compare to your critical value(s) d. State your decision based on the results e. Write a conclusion statement that clearly expresses what your decision means f. What is the probability that you have committed a Type 1 error? g. How could you change your approach to this hypothesis test to decrease the chances of making a Type 1 error? (Hint: Focus on step b) h. Does decreasing the chances of making a Type 1 error make it easier or harder to reject the Null Hypothesis? What evidence are you using to make your decision?
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
Transcribed Image Text:**Scenario:**
You are a bank manager and you want to secure a raise for your bank tellers. The board of trustees show you financial data indicating that 15 customers a day is the average number of clients served for bank tellers in your region. If you can provide convincing evidence that your bank tellers are actually serving a greater number of clients per day, they will grant a 10% raise. Over the next week, you measure the average number of customers served by the 31 bank tellers at your local branch and determine that their average is 20 customers a day with a standard deviation of 3. Do you have sufficient evidence to argue for a raise?
**Tasks:**
a. Write out the null and alternative/research hypothesis.
b. Using the .05 level of significance, find the critical value(s) and sketch the comparison distribution with rejection region(s) shaded in.
c. Calculate the value of the test statistic that you will then compare to your critical value(s).
d. State your decision based on the results.
e. Write a conclusion statement that clearly expresses what your decision means.
f. What is the probability that you have committed a Type 1 error?
g. How could you change your approach to this hypothesis test to decrease the chances of making a Type 1 error? (Hint: Focus on step b)
h. Does decreasing the chances of making a Type 1 error make it easier or harder to reject the Null Hypothesis? What evidence are you using to make your decision?
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 7 steps with 1 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