Exam 10: Statistical Inference About Means and Proportions With Two Populations

In order to estimate the difference between the yearly incomes of marketing managers in the East and West of the United States,the following information was gathered. a.Develop an interval estimate for the difference between the average yearly incomes of the marketing managers in the East and West.Use $\alpha$ = 0.05. b.At 95% confidence,use the p-value approach and test to determine if the average yearly income of marketing managers in the East is significantly different from the West.

A credit company has gathered information regarding the average amount owed by people under 30 years old and by people over 30 years.Independent random samples were taken from both age groups.You are given the following information. Construct a 95% confidence interval for the difference between the average amounts owed by the two age groups.

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.

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

Babies weighing less than 5.5 pounds at birth are considered "low-birth-weight babies." In the United States,7.6% of newborns are low-birth-weight babies.The following information was accumulated from samples of new births taken from two counties. a.Develop a 95% confidence interval estimate for the difference between the proportions of low-birth-weight babies in the two counties. b.Is there conclusive evidence that one of the proportions is significantly more than the other? If yes,which county? Explain,using the results of part (a).Do not perform any test.

During the primary elections of 1996,candidate A showed the following pre-election voter support in Tennessee and Mississippi. a.Develop a 95% confidence interval estimate for the difference between the proportion of voters favoring candidate A in the two states. b.Is there conclusive evidence that one of the two states had a larger proportion of voters' support? If yes,which state? Explain.

In order to estimate the difference between the average mortgages in the southern and the northern states 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.

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.

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

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card.You are given the following information. -Refer to Exhibit 10-6.A 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card.You are given the following information. -Refer to Exhibit 10-6.A point estimate for the difference between the mean purchases of the users of the two credit cards 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.

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. -Refer to Exhibit 10-1.The standard error for the difference between the two means 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 p-value for the difference between the two population means is

The following information regarding the ages of full-time and part-time students are given.Using the following data,develop an interval estimate for the difference between the mean ages of the two populations.Use a 5% level of significance.The degrees of freedom for the t distribution is 106.

A random sample of 89 tourists in Chattanooga showed that they spent an average of $2,860 (in a week)with a standard deviation of $126;and a sample of 64 tourists in Orlando showed that they spent an average of $2,935 (in a week)with a standard deviation of $138.We are interested in determining if there is any significant difference between the average expenditures of those who visited the two cities? a.Determine the degrees of freedom for this test. b.Compute the test statistic. c.Compute the p-value. d.What is your conclusion? Let $\alpha$ = .05.

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.

The business manager of a local health clinic is interested in estimating the difference between the fees for extended office visits in her center and the fees of a newly opened group practice.She gathered the following information regarding the two offices. Develop a 95% confidence interval estimate for the difference between the average fees of the two offices.

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card.You are given the following information. -Refer to Exhibit 10-6.At 95% confidence,the margin of error is

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