Exam 10: Inference About Means and Proportions With Two Populations

Samples of employees of Companies A and B provided the following information regarding the ages of employees. Develop a 97% confidence interval for the difference between the average ages of the employees of the two companies.

The results of a recent poll on the preference of voters regarding presidential candidates are shown below. At 95% confidence, test to determine whether or not there is a significant difference between the preferences for the two candidates.

Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. -Refer to Exhibit 10-10. The point estimate for the difference between the two population proportions in favor of this product is

In a random sample of 200 Republicans, 160 opposed the new tax laws. While in a sample of 120 Democrats, 84 opposed the new tax laws. Determine a 95% confidence interval estimate for the difference between the proportions of Republicans and Democrats opposed to this new law.

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.

Among a sample of 50 M.D.'s (medical doctors) in the city of Memphis, Tennessee, 10 indicated they make house calls; while among a sample of 100 M.D.'s in Atlanta, Georgia, 18 said they make house calls. Determine a 95% interval estimate for the difference between the proportion of doctors who make house calls in the two cities.

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. -Refer to Exhibit 10-9. The test statistic is

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. -Refer to Exhibit 10-1. The 95% confidence interval for the difference between the means of the two populations is

The following are the test scores of two samples of students from University A and University B on a national statistics examination. Develop a 95% confidence interval estimate for the difference between the mean scores of the two populations.

Exhibit 10-13 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. -Refer to Exhibit 10-13. The point estimate of the difference between the means is

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. -Refer to Exhibit 10-1. If you are interested in testing whether or not the average salary of males is significantly greater than that of females, the test statistic is

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. -Refer to Exhibit 10-3. The test statistic for the difference between the two population means is

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.

Consider the following results for two samples randomly taken from two populations. a.What are the degrees of freedom for the t distribution? b.At 95% confidence, compute the margin of error. c.Develop a 95% confidence interval for the difference between the two population means.

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.

In order to estimate the difference between the average yearly salaries of top managers in private and governmental organizations, the following information was gathered. Develop an interval estimate for the difference between the average salaries of the two sectors. Let $\alpha$ = .05.

Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. -Refer to Exhibit 10-10. At 95% confidence, the margin of error is

Exhibit 10-5 The following information was obtained from matched samples. -Refer to Exhibit 10-5. The null hypothesis tested is H₀: $\mu$ _d = 0. The test statistic for the difference between the two population means is

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. -Refer to Exhibit 10-9. At 90% confidence the null hypothesis

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