Exam 10: Inference About Means and Proportions With Two Populations

Exhibit 10-4 The following information was obtained from independent random samples.Assume normally distributed populations with equal variances. -Refer to Exhibit 10-4. The standard error of is

Recently, a local newspaper reported that part time students are older than full time students. In order to test the validity of its statement, two independent samples of students were selected. a.Give the hypotheses for the above. b.Determine the degrees of freedom. c.Compute the test statistic. d.At 95% confidence, test to determine whether or not the average age of part time students is significantly more than full time students.

Consider the following results for two samples randomly taken from two populations. a.Determine the degrees of freedom for the t distribution. b.Develop a 95% confidence interval for the difference between the two population means. c.Is there conclusive evidence that one population has a larger mean? Explain.

In order to estimate the difference between the average mortgages in the South and the North of the United States, the following information was gathered. a.Compute the degrees of freedom for the t distribution. b.Develop an interval estimate for the difference between the average of the mortgages in the South and North. Let Alpha = 0.03.

Exhibit 10-11 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. We are interested in determining if the accident proportions differ between the two age groups. -Refer to Exhibit 10-11. The pooled proportion is

In a sample of 40 Democrats, 6 opposed the President's foreign policy, while of 50 Republicans, 8 were opposed to his policy. Determine a 90% confidence interval estimate for the difference between the proportions of the opinions of the individuals in the two parties.

A movie based on a best-selling novel was recently released. Six hundred viewers of the movie, 235 of whom had previously read the novel, were asked to rate the quality of the movie. The survey showed that 141 of the novel readers gave the movie a rating of excellent, while 248 of the non-readers gave the movie an excellent rating. a. Develop an interval estimate of the difference between the proportions of the two populations, using a .05 level of significance, as the basis for your decision. b. Can we conclude, on the basis of a hypothesis test about p₁ - p₂, that the proportion of the non-readers of the novel who thought the movie was excellent is greater than the proportion of readers of the novel who thought the movie was excellent? Use a .05 level of significance. (Hint: this is a one-tailed test.)

Zip, Inc. manufactures Zip drives on two different manufacturing processes. Because the management of this company is interested in determining if process 1 takes less manufacturing time, they selected independent samples from each process. The results of the samples are shown below. a.State the null and alternative hypotheses. b.Determine the degrees of freedom for the t test. c.Compute the test statistic d.At 95% confidence, test to determine if there is sufficient evidence to indicate that process 1 takes a significantly shorter time to manufacture the Zip drives.

Exhibit 10-7 In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. -Refer to Exhibit 10-7. A 95% interval estimate for the difference between the two population means is

A comparative study of organic and conventionally grown produce was checked for the presence of E. coli. Results are summarized below. Is there a significant difference in the proportion of E. Coli in organic vs. conventionally grown produce? Test at $\alpha$ = 0.10.

The standard error of is the

The following data present the number of computer units sold per day by a sample of 6 salespersons before and after a bonus plan was implemented. At 95% confidence, test to see if the bonus plan was effective. That is, did the bonus plan actually increase sales?

Consider the following hypothesis test: The following results are for two independent samples taken from two populations. a.Determine the degrees of freedom for the t distribution. b.Compute the test statistic. c.Determine the p-value and test the above hypotheses.

Independent random samples taken at two companies provided the following information regarding annual salaries of the employees. a.We want to determine whether or not there is a significant difference between the average salaries of the employees at the two companies. Compute the test statistic. b.Compute the p-value; and at 95% confidence, test the hypotheses.

Exhibit 10-12 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. -Refer to Exhibit 10-12. The standard error of is

Exhibit 10-2 The following information was obtained from matched samples.The daily production rates for a sample of workers before and after a training program are shown below. -Refer to Exhibit 10-2. The point estimate for the difference between the means of the two populations is

Allied Corporation is trying to determine whether to purchase Machine A or B. It has leased the two machines for a month. A random sample of 5 employees has been taken. These employees have gone through a training session on both machines. Below you are given information on their productivity rate on both machines. (Let the difference "d" be d = A - B.) a.State the null and alternative hypotheses for a two-tailed test. b.Find the mean and standard deviation for the difference. c.Compute the test statistic. d.Test the null hypothesis stated in Part a at the 10% level.

A company attempts to evaluate the potential for a new bonus plan by selecting a sample of 4 salespersons to use the bonus plan for a trial period. The weekly sales volume before and after implementing the bonus plan is shown below. (For the following matched samples, let the difference "d" be d = after - before.) a.State the hypotheses. b.Compute the test statistic. c.Use Alpha = .05 and test to see if the bonus plan will result in an increase in the mean weekly sales.

Independent simple random samples are taken to test the difference between the means of two populations whose variances are not known. The sample sizes are n₁ = 32 and n₂ = 40. The correct distribution to use is the

A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken five years ago. Results are summarized below. Has the proportion increased significantly? Let $\alpha$ = 0.05.