Exam 10: Hypothesis Testing: Two Sample Tests

If you are testing for the difference between the means of two independent populations with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to

Instruction 10-12 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 Instruction 10-12,the critical values for a two-tailed test of the null hypothesis of no difference in the population means at the α = 0.05 level of significance are ________.

A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination.A group of 50 men (group 1)and 40 women (group 2)were asked if they thought sexual discrimination is a problem in Australia.Of those sampled,11 of the men and 19 of the women did believe that sexual discrimination is a problem.If the p-value turns out to be 0.035 (which is NOT the real value in this data set),then

Instruction 10-9 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course.The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course.The groups are assumed to be independent random samples.Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study,respectively. -Referring to Instruction 10-9,if the firm wanted to test whether a greater proportion of workers would currently like to attend a self-improvement course than in the past,which represents the relevant hypotheses?

Instruction 10-13 To investigate the efficacy of a diet,a random sample of 16 male patients is drawn 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 kilograms with the standard deviation of differences computed as 6.0 kilograms. -Referring to Instruction 10-13,what is the 95% confidence interval estimate for the mean difference in weight before and after the diet?

Instruction 10-13 To investigate the efficacy of a diet,a random sample of 16 male patients is drawn 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 kilograms with the standard deviation of differences computed as 6.0 kilograms. -Referring to Instruction 10-13,there are ________ degrees of freedom for this test.

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

Instruction 10-12 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 Instruction 10-12,if you were interested in testing against the one-tailed alternative that μ₁ > μ₂ at the α = 0.01 level of significance,the null hypothesis would ________ .

Instruction 10-9 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course.The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course.The groups are assumed to be independent random samples.Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study,respectively. -Referring to Instruction 10-9,construct a 99% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study.

Instruction 10-11 A quality control engineer is in charge of the manufacture of computer disks.Two different processes can be used to manufacture the disks.He suspects that the Kohler method produces a greater proportion of defects than the Russell method.He samples 150 of the Kohler and 200 of the Russell disks and finds that 27 and 18 of them,respectively,are defective.If Kohler is designated as "Group 1" and Russell is designated as "Group 2",perform the appropriate test at a level of significance of 0.01. -Referring to Instruction 10-11,the null hypothesis should be rejected.

Instruction 10-9 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course.The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course.The groups are assumed to be independent random samples.Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study,respectively. -Referring to Instruction 10-9,what is the unbiased point estimate for the difference between the two population proportions?

When testing for differences between the means of two related populations,you can use either a one-tailed or two-tailed test.

Instruction 10-9 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course.The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course.The groups are assumed to be independent random samples.Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study,respectively. -Referring to Instruction 10-9,what is the estimated standard error of the difference between the two sample proportions?

Instruction 10-10 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day.He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors.In a random sample of 100 of each type of major at graduation,he found that 65 accounting students and 52 economics students had job offers.If the accounting students are designated as "Group 1" and the economics students are designated as "Group 2",perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Instruction 10-10,the value of the test statistic is ________.

For all two-sample tests,the sample sizes must be equal in the two groups.

All F tests are one-tailed tests.

When the sample sizes are equal,the pooled variance of the two groups is the average of the two sample variances.

The t test for the difference between the means of two independent populations assumes that the respective

Instruction 10-9 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course.The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course.The groups are assumed to be independent random samples.Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study,respectively. -Referring to Instruction 10-9,construct a 90% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study.

Instruction 10-11 A quality control engineer is in charge of the manufacture of computer disks.Two different processes can be used to manufacture the disks.He suspects that the Kohler method produces a greater proportion of defects than the Russell method.He samples 150 of the Kohler and 200 of the Russell disks and finds that 27 and 18 of them,respectively,are defective.If Kohler is designated as "Group 1" and Russell is designated as "Group 2",perform the appropriate test at a level of significance of 0.01. -Referring to Instruction 10-11,construct a 99% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.