Exam 10: Hypothesis Testing: Additional Topics

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: From the top 1000 companies in valuation,a comparison of the mean dividend yield of the top and bottom ten electric utility companies is desired.Let 1 = top ten,and 2 = bottom ten,electric utility companies respectively.The data shown below are for two independent samples,which are drawn at random from populations that are normally distributed. -Use Excel or Minitab to conduct a two-sample t-test for data in the table above.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose two food 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 16 cuts of fresh meat are treated with preservative A and another 12 cuts of meat are treated with preservative B.The number of hours until spoilage begins is recorded for each of the 28 cuts of meat.The results are summarized in the table below. -The numerator and denominator degrees of freedom associated with the test statistic for determining if there is a difference in the population variances for preservatives A and B are,respectively:

Given H₁ : μ_x - μ_y < 0,the hypothesis test is a(n):

If testing for the difference between the means of two related populations,the appropriate null hypothesis is:

What can the researcher conclude?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: To investigate the effectiveness of a diet,a random sample of 16 female patients is drawn from a population of adult females using the diet.The weight of each individual in the sample is taken at the start and at the end of the diet.Assume that the population of differences in weight before and after the diet follows a normal distribution.Suppose the mean decrease in weights over all 16 subjects in the study is 4.0 pounds with the standard deviation of differences computed as 6.4 pounds.Let µ_x - µ_y = mean weight before the diet - mean weight after the diet. -In order to test if the diet is effective,what is the value of the test statistic?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The following data were generated from a matched pairs experiment. -A university vice president for academic affairs randomly selects 15 tenured faculty from the College of Education and 15 tenured faculty from the College of Business.Each faculty member is then asked to rate his or her job satisfaction on a scale of 1 (very dissatisfied)to 5 (very satisfied).Is this an example of independent samples or dependent samples? Explain.

Which of the following is an appropriate null hypothesis?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A trap and skeet shooting club,purchases clay pigeons.These are quite fragile and often break in the box during shipment without any outward sign of damage.Even as the clay pigeons are loaded into the throwing machine,broken or cracked clay pigeons may not be noticed.Each clay pigeon broken is a net loss to the club so the club is anxious to purchase from suppliers who have a record of little or no breakage in shipping and handling.Two suppliers of clay pigeons are contacted and asked for price quotes.Supplier 1 quotes a higher price than Supplier 2 but says that the higher price is the result of better,more expensive packaging and thus results in more usable clay pigeons per case.The shooting club manager decides to purchase 10 cases from each supplier.Each case has 250 clay pigeons.Careful records are maintained on each case as to the number of good clay pigeons.The records after the cases were used are as follows: Number of good clay pigeons -Using results of Excel or Minitab to conduct a two-sample t-test,test H₀ : μ₁ - μ₂ ≤ 0 vs.H₁ : μ₁ - μ₂ > 0 at the 5% significance level.

What is the critical value(s)for this test? (Hint: Use Excel to find the critical value(s))

In a recent market research survey,college students were asked the amount of time (in hours)they spend weekly watching television and surfing on the Internet.The researchers were interested in determining whether the time spent on each activity was equal.They collected the following data: Do you have reason to believe that students spend the same amount of time on average watching television as they do on the Internet? (Assume 10% level of significance)

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: From the top 1000 companies in valuation,a comparison of the mean dividend yield of the top and bottom ten electric utility companies is desired.Let 1 = top ten,and 2 = bottom ten,electric utility companies respectively.The data shown below are for two independent samples,which are drawn at random from populations that are normally distributed. -Using results of Excel or Minitab to conduct a two-sample t-test for data in the table above,test H₀ : μ₁ - μ₂ = 0 vs.H₁ : μ₁ - μ₂ ≠ 0 at the 5% significance level.What is your conclusion?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: From the top 1000 companies in valuation,a comparison of the mean dividend yield of the top and bottom ten electric utility companies is desired.Let 1 = top ten,and 2 = bottom ten,electric utility companies respectively.The data shown below are for two independent samples,which are drawn at random from populations that are normally distributed. -25 consumers were provided with a package containing two different brands of instant coffee.A week later,they were asked to rate the taste of each coffee on a scale of 1 (poor taste)to 10 (excellent taste).Is this an example of independent samples or dependent samples? Explain.

When testing for the difference between the means of two normal populations using two independent samples with equal variances and with sizes of n_x = 20 and n_y = 15,what is the number of degrees of freedom for the t test statistic?

In testing for the differences between the means of two independent populations,we assume that the 2 populations each follow a normal distribution.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose two food 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 16 cuts of fresh meat are treated with preservative A and another 12 cuts of meat are treated with preservative B.The number of hours until spoilage begins is recorded for each of the 28 cuts of meat.The results are summarized in the table below. -The most accurate statement that can be made about the p-value for testing whether there is a difference in the population variances for preservatives A and B is:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The sociological department of Kent College conducted an investigation to determine how long it takes for a woman or man to get married after their graduation in Kent Town.Two independent random samples were selected and the following summary information concerning times to completion of medical school were computed: -Perform the appropriate test of hypothesis to determine whether there is a significant difference in time to completion of medical school between women and men.Test using α = 0.05.

For two independent random samples that each follows a normal distribution,if the population variances are equal,then the random variable F is calculated using the formula:

Given the following information, = 4, = 6,n₁ = 16,n₂ = 25,calculate the pooled sample variance that should be used in the pooled-variance t test.

What is the cutoff point for an F distribution with 10 numerator degrees of freedom and 13 denominator degrees of freedom at α = 0.01?