Exam 10: Two-Sample Tests

SCENARIO 10-5 To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below. -Referring to Scenario 10-5,in examining the differences between related samples we are essentially sampling from an underlying population of difference "scores."

SCENARIO 10-9 The following EXCEL output contains the results of a test to determine whether the proportions of satisfied customers at two resorts are the same or different. Two-Sample Tests 10-31 -Referring to Scenario 10-9, if you want to test the claim that "Resort 1 (Group 1) has a lower proportion of satisfied customers compared to Resort 2 (Group 2)", you will use

SCENARIO 10-3 A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: x̄ _G = 35 months,S_G ² = 900 Metropolis: x̄ _M = 50 months,S _M² = 1050 -Referring to Scenario 10-3,suppose α = 0.05.Which of the following represents the result of the relevant hypothesis 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. t-Test: Two-Sample Assuming Unequal Variances Two-Sample Tests 10-41 -Referring to Scenario 10-13,what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.05?

If we wish to determine whether there is evidence that the proportion of items of interest is higher in Group 1 than in Group 2,and the test statistic for Z = -2.07 where the difference is defined as Group 1's proportion minus Group 2's proportion,the p-value is equal to .

The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women.The article claimed that women perceived the problem to be much more prevalent than did men.One question asked to both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" Some 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 men were interviewed.For a 0.01 level of significance,what is the critical value for the rejection region?

SCENARIO 10-14 The use of preservatives by food processors has become a controversial issue.Suppose two preservatives are extensively tested and determined safe for use in meats.A processor wants to compare the preservatives for their effects on retarding spoilage.Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II,and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat.The results are summarized in the table below. -Referring to Scenario 10-14,suppose α = 0.05.Which of the following represents the correct conclusion?

In testing for the differences between the means of two related populations,the hypothesis is the hypothesis of "no differences."

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

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,what is the 95% confidence interval estimate for the difference between two means?

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. t-Test: Two-Sample Assuming Unequal Variances Two-Sample Tests 10-41 -Referring to Scenario 10-13,what is the largest level of significance at which a test on a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels will not be rejected?

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. 10-20 Two-Sample Tests -Referring to Scenario 10-7,what is the 90% confidence interval estimate for the mean difference in prices?

The statistical distribution used for testing the difference between two population variances is the _____ distribution.

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. 10-20 Two-Sample Tests -Referring to Scenario 10-7,what is the 95% confidence interval estimate for the mean difference in prices?

SCENARIO 10-5 To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below. -Referring to Scenario 10-5,at the 0.05 level of significance,the conclusion for this hypothesis test is that there is sufficient evidence that:

SCENARIO 10-3 A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: x̄ _G = 35 months,S_G ² = 900 Metropolis: x̄ _M = 50 months,S _M² = 1050 -Referring to Scenario 10-3,suppose α = 0.01.Which of the following represents the result of the relevant hypothesis 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. t-Test: Two-Sample Assuming Unequal Variances Two-Sample Tests 10-41 -Referring to Scenario 10-13,suppose α = 0.05.Which of the following represents the correct conclusion?

F tests are one-tail tests.

SCENARIO 10-4 Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. -Referring to Scenario 10-4,the critical values for a two-tail test of the null hypothesis of no difference in the population means at the ? = 0.05 level of significance are .

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. t-Test: Two-Sample Assuming Unequal Variances Two-Sample Tests 10-41 -Referring to Scenario 10-13,suppose = 0.10.Which of the following represents the result of the relevant hypothesis test?