Exam 10: Hypothesis Testing: Additional Topics

When testing H₀ : μ₁ - μ₂ = 0 against H₁ : μ₁ - μ₂ ≠ 0,the observed value of the Z-score was found to be -2.13.The p-value for this test would be 0.4668.

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 summarize the data using descriptive statistics.

In testing for the differences between the means of two related populations,we assume that the differences follow a t distribution.

In a hypothesis test of the difference between two population means,if the probability of Type II error is 0.25,then:

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 appropriate statistical test?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A manager is considering the purchase of new production equipment to improve the output of the plant.Suppose the equipment from two suppliers is extensively tested in multiple production runs.A total of 20 runs are recorded on Supplier A's equipment and another 15 runs are reported from Supplier B's equipment.The volume produced is recorded for each of the 35 runs.The results are summarized in the table below. -The value of the test statistic for determining if there is a difference in the population variances for Supplier A and B is equal to:

What is the pooled variance?

Repeated measurements collected from the same individuals is an example of data collected from two related populations.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: As part of its quality control program,the Scullia Auto Company (SAC)began inspecting all supplier shipments of steel bars and recording the defect rate according to quality criteria such as strength,dimensional characteristics,etc.When SAC began this program,the defect rate in 100 shipments averaged 9%.A recent report indicated an average defect rate of 2.2% in 136 shipments.The quality control department wants to determine,at the 0.05 level of significance,if this represents a significant improvement in the quality of the steel. -What is the p-value?

What is the value of α,if the cutoff point for an F distribution F_4,8 = 7.01?

If testing for the difference between the means of two related populations,with samples of sizes n₁ = n₂ = n,where the variance of the differences is unknown,what is the number of degrees of freedom?

If the null hypothesis H₀ : μ_x - μ_y ≤ 0 is rejected against the alternative H₁ : μ_x - μ_y > 0 at the 5% level of significance,then using the same data,it must be rejected against that alternative at the 1% level.

The test of equality of the variances between two normally distributed populations relies on the random variable which has a(n):

An F distribution is an example of a symmetrical distribution.

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 -Use Excel or Minitab to conduct a two-sample t-test.

A random sample of 1500 people from the town of Sotown were asked if they thought that the Boston Red Sox would win the next World Series.78% of the sample thought that the Boston Red Sox would win.But when a random sample of 1500 people from the town of Michika was asked the same question,65% thought that the Boston Red Sox would win the next World Series.Does this provide strong evidence at the 5% significance level that the people in Sotown are more optimistic about the Boston Red Sox's chances of winning the next World Series?

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. -What assumptions are necessary for a comparison of the population variances to be valid?

The t test for the mean difference between two related populations assumes that the:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: As part of its quality control program,the Scullia Auto Company (SAC)began inspecting all supplier shipments of steel bars and recording the defect rate according to quality criteria such as strength,dimensional characteristics,etc.When SAC began this program,the defect rate in 100 shipments averaged 9%.A recent report indicated an average defect rate of 2.2% in 136 shipments.The quality control department wants to determine,at the 0.05 level of significance,if this represents a significant improvement in the quality of the steel. -State the null and alternative hypotheses.

If testing the difference between the means of two related populations with samples of sizes n₁ = 16 and n₂ = 16,what is the number of degrees of freedom?