E270 Homework Assignment 11 - Module 11

Warning:If you do not show your work on this assignment, you will not get credit for any answers, even if they are correct.

1.A bank with a branch located in Valparaiso has been receiving complaints regarding the wait time to talk to a loan officer.A second branch, located in Crown Point, has not received the same complaints.The manager of both branches state that their process is fine, but you, as the VP in charge of both branches, wants to investigate the difference between the two branches with respect to waiting times.

You collect a random sample of n=30 from each bank with the following results (time was recorded in minutes).

You are interested in conducting a 2 Sample t test to determine if there is a difference in the mean wait time.The test will be conducted at the 0.05 level of significance (95% confidence level).

a. What assumption is required for you to conduct this test?Do you feel that the assumption is valid?

b.What is the null and alternative hypothesis you will use in this test?

c.Assuming that the population variances from both branches are equal, is there evidence that the mean waiting time is different between the two banks?Defend your answer using both the confidence interval and the p-value.

d.Interpret the p-value.

e.Interpret the confidence interval.

2.Would your answer change for Question 1, part b above if you had assumed unequal variances?Defend you answer using the p-value and confidence interval.

3.Using the data from Question 1 above, is there evidence that there is a difference in the variability of the waiting times between the two banks?Assume that the normality assumption for both populations is valid. State your null and alternative hypothesis and defend your answer using the p-value and confidence interval.

4.Based on the results of questions 1 through 3 above, what would be your decision, and action, as the VP of the banks?

5.Are you an impulse shopper?A survey of 500 shoppers at the Mall (250 male and 250 female) indicated that 80 of the males and 100 of the females make an impulse purchase every time they shop.

a.In order to answer this question, what statistical test will be used?

b.What assumption is necessary to conduct the test you stated in part a?Do you feel this assumption is valid?

c.What is the null and alternative hypothesis you will use for the test you stated in part a above?

d.At the 0.05 level of significance (95% confidence level), is there evidence of a difference in proportion between males and females regarding making impulse purchases? Defend your answer using the p-value and confidence interval.

e.What is the interpretation of the confidence interval in this case?

6.Over the past year, you, as the vice president for human resources at a large medical center, has run a series of three-month workshops aimed at increasing worker motivation and performance.To check the effectiveness of the workshops, you selected a random sample of 35 employees from the personnel files.You collected the employee performance ratings recorded before and after workshop attendance and stored the paired ratings in the Excel data file for this assignment under the tab Perform.

a.In order to answer this question, what statistical test will be used?

b.What assumption is necessary to conduct the test you stated in part a?Do you feel this assumption is valid?

c.What is the null and alternative hypothesis you will use for the test you stated in part a?

d.At the 0.05 level of significance (95% confidence level), is there evidence of an improvement in the test scores?Defend your answer using the p-value and confidence interval.

e.Interpret the confidence interval in this case.

f.Assuming the training was expensive, as the VP of HR, do you feel your analysis supports continuing the training?Explain your answer.

7.Using your travel data, using a 0.05 level of significance.Assume your travel times are normally distributed.

a.Determine if there is a difference in the variability of travel times between your "to work" data and your "to home" data.(alternatively, "lunch" and "dinner").

b.Using the appropriate test, determine if there is a difference in the mean time between your two data sets.