Exam 10: Hypothesis Testing: Additional Topics

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 43.5 and standard deviation of 4.1 while the second sample has a mean of 40.1 and standard deviation of 3.2.A researcher would like to test if there is a difference between the population means at the 0.05 significance level. -State the null hypothesis.

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 value of the test statistic for determining if there is a difference in the population variances for preservatives A and B is equal to:

The procedure that utilizes the normal distribution to test the difference between two population proportions is valid for all sample sizes.

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 critical value(s)at the 0.05 level of significance?

What is the value of the test statistic?

The test statistic for the equality of two population variances is based on the:

In a random sample of 150 music industry management majors,75 rated a sense of humor as very important trait to their career performance.The same view was held by 81 of an independent random sample of 180 professional golf management majors.Test at the 5% level against a two-sided alternative the null hypothesis that the population proportions of music industry management and professional golf management majors who rate a sense of humor as very important are the same.

When testing for the difference between the means of two independent populations with equal variances and with samples of sizes n₁ = 20 and n₂ = 20,what is the number of degrees of freedom?

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 test statistic?

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: -Find the p-value associated with the test of hypothesis to determine whether there is a significant difference in time to completion of medical school between women and men and explain how to use it for testing the hypothesis using α = 0.05.

Hypothesis tests that use the F distribution do not depend on the assumption that the populations are normally distributed as long as the sample sizes are large.

For two independent random samples with n_x and n_y observations,and each following a normal distribution,which of the following would be the F distribution degrees of freedom in the numerator?

In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves?

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

When testing for differences between the means of two independent populations,only a t-test can be used.

To use the Student's t distribution to compare population means when the population variances are unknown and sample sizes are small,the populations are assumed to be normally distributed.

Assuming the independent samples procedure was used,which of the following is the correct test statistic.

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 alternative hypothesis?

When testing for the difference between the means of two independent populations,with samples of sizes n₁ and n₂,where the population variances are unknown but assumed to be equal,what is the number of degrees of freedom?

When testing for the difference between two population variances with sample sizes of n₁ = 10 and n₂ = 12,what is (are)the number (s)of degrees of freedom?