Exam 10: Two-Sample Tests

True or False: A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen.The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal.For this situation, the professor should use a t test with independent samples.

SCENARIO 10-3 -Referring to Scenario 10-3, which of the following represents the relevant hypotheses tested by The real estate company?

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 99% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

True or False: When testing for differences between the means of 2 related populations, you can use either a one-tail or two-tail test.

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 10-1 Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility.The SSATL scores are summarized below. -Referring to Scenario 10-1, what is the value of the test statistic?

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

SCENARIO 10-3 -

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, the t test should be _______-tail.

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. What assumptions were necessary to conduct this hypothesis test?

The t test for the difference between the means of 2 independent populations assumes that the Respective

SCENARIO 10-3 -Referring to Scenario 10-3, suppose = 0.05.Which of the following represents the result of the Relevant hypothesis test?

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 10-3 -Referring to Scenario 10-3, suppose = 0.01.Which of the following represents the correct Conclusion?

SCENARIO 10-3 -Referring to Scenario 10-3, what is(are)the critical value(s)of the relevant hypothesis test if the Level of significance is 0.05?

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 90% confidence interval estimate for the difference between two means?

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. 10-32 Two-Sample Tests -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 10-4 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 _______.

True or False: In testing the difference between two proportions using the normal distribution, you may use a two-tail Z test.

SCENARIO 10-3 -Referring to Scenario 10-3, what is a point estimate for the mean of the sampling distribution of The difference between the 2 sample means?