Exam 10: Two-Sample Tests

SCENARIO 10-13 The amount of time required to reach a customer service representative has a huge impact on customer satisfaction.Below is the Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels.Assume that the population variances in the amount of time for the two hotels are not equal. -Referring to Scenario 10-13, what is the value of the test statistic for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels?

A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. The result of the pooled-variance t-test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given below. -Referring to Scenario 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.The proper conclusion for this test is:

SCENARIO 10-8 A few years ago, Pepsi invited consumers to take the "Pepsi Challenge." Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test.Pepsi was interested in determining what factors played a role in people's taste preferences.One of the factors studied was the gender of the consumer.Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi. -Referring to Scenario 10-8, suppose that the two-tail p-value was really 0.0734.State the proper conclusion.

SCENARIO 10-8 A few years ago, Pepsi invited consumers to take the "Pepsi Challenge." Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test.Pepsi was interested in determining what factors played a role in people's taste preferences.One of the factors studied was the gender of the consumer.Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi. -Referring to Scenario 10-8, construct a 95% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

The F test used for testing the difference in two population variances is always a one-tail test.

SCENARIO 10-13 The amount of time required to reach a customer service representative has a huge impact on customer satisfaction.Below is the Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels.Assume that the population variances in the amount of time for the two hotels are not equal. -Referring to Scenario 10-13, what is the standardized value of the estimate of the mean of the sampling distribution for the difference between sample means?

Given the following information, calculate the degrees of freedom that should be used in the pooled-variance t test.

SCENARIO 10-2 A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries.Of primary interest to the researcher was the effect of gender on starting salaries.The result of the pooled-variance t-test of the mean salaries of the females (Population 1)and males (Population 2)in the sample is given below. -Referring to Scenario 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.Which of the following is an appropriate alternative hypothesis?

SCENARIO 10-10 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self- improvement course would like such a course.The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course.The groups are assumed to be independent random samples.Let and represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. -Referring to Scenario 10-10, what is/are the critical value(s)when testing whether population proportions are different if = 0.10?

A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. The result of the pooled-variance t-test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given below. -Referring to Scenario 10-2, what is the 90% confidence interval estimate for the difference between two means?

SCENARIO 10-11 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day.He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors.In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Scenario 10-12, the hypotheses the dean should use are:

SCENARIO 10-11 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day.He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors.In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Scenario 10-11, the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

SCENARIO 10-8 A few years ago, Pepsi invited consumers to take the "Pepsi Challenge." Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test.Pepsi was interested in determining what factors played a role in people's taste preferences.One of the factors studied was the gender of the consumer.Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi. -Referring to Scenario 10-8, suppose Pepsi wanted to test to determine if the males preferred Pepsi less than the females.Using the test statistic given, compute the appropriate p-value for the test.

SCENARIO 10-15 The table below presents the summary statistics for the starting annual salaries (in thousands of dollars)for individuals entering the public accounting and financial planning professions. Test whether the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning assuming that the two population variances are the same. -Referring to Scenario 10-15, which of the following represents the relevant hypotheses tested?

SCENARIO 10-7 A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials.He wants to compare these prices with those of his primary supplier.The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01. -Referring to Scenario 10-7, what is the 95% confidence interval estimate for the mean difference in prices?

SCENARIO 10-6 To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet.The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later.Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t-test for related samples can be used to determine if there was a significant decrease in the mean weight during this period.Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds. -Referring to Scenario 10-6, there are _______ degrees of freedom for this test.

SCENARIO 10-11 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day.He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors.In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Scenario 10-11, the p-value of the test is ________.

In testing for differences between the means of two independent populations, the null hypothesis is:

SCENARIO 10-11 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day.He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors.In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Scenario 10-11, the same decision would be made with this test if the level of significance had been 0.10 rather than 0.05.

SCENARIO 10-12 A quality control engineer is in charge of the manufacture of USB flash drives.Two different processes can be used to manufacture the flash drives.He suspects that the Kohler method produces a greater proportion of defects than the Russell method.He samples 150 of the Kohler and 200 of the Russell flash drives and finds that 27 and 18 of them, respectively, are defective. If Kohler is designated as "Group 1" and Russell is designated as "Group 2," perform the appropriate test at a level of significance of 0.01. -Referring to Scenario 10-12, the same decision would be made if this had been a two-tail test at a level of significance of 0.01.