Exam 10: Inference About Means and Proportions With Two Populations

The office of records at a university has stated that the proportion of incoming female students who major in business has increased. A sample of female students taken several years ago is compared with a sample of female students this year. Results are summarized below. Has the proportion increased significantly? Test at alpha = .10.

Of 150 Chattanooga residents surveyed, 60 indicated that they participated in a recycling program. In Knoxville, 120 residents were surveyed and 36 claimed to recycle. a.Determine a 95% confidence interval estimate for the difference between the proportion of residents recycling in the two cities. b.From your answer in Part a, is there sufficient evidence to conclude that there is a significant difference in the proportion of residents participating in a recycling program?

Exhibit 10-5 The following information was obtained from matched samples. -Refer to Exhibit 10-5. If the null hypothesis is tested at the 5% level, the null hypothesis

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.

Of 300 female registered voters surveyed, 120 indicated they were planning to vote for the incumbent president; while of 400 male registered voters, 140 indicated they were planning to vote for the incumbent president. a.Compute the test statistic. b.At alpha = .05, test to see if there is a significant difference between the proportions of females and males who plan to vote for the incumbent president. (Use the p-value approach.)

A company wants to identify which of two production methods has the smaller completion time. One sample of workers is selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on

The following information regarding the number of semester hours taken from random samples of day and evening students is provided. Develop a 95% confidence interval estimate for the difference between the mean semester hours taken by the two groups of students.

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.

Starting annual salaries for business school graduates majoring in finance and management information systems (MIS) were collected in two independent random samples summarized below. Based on previous studies, the population standard deviations for Finance and MIS salaries are estimated to be $2,100 and $2,600, respectively.Finance MIS n₁ = 60 n₂ = 50 = $43,200 = $46,500 a. Develop a 95% confidence interval estimate of the difference between the starting salaries for the two majors. b. Using $\alpha$ = .10, test to determine if the average starting salary for an MIS graduate is $4,000 more than the starting salary for a finance graduate. Use both the critical value and p-value approaches to hypothesis testing. (Hint: the null hypothesis is H₀: $\mu$ ₁ - $\mu$ ₂ = $4,000, where $\mu$ ₁ is the average starting salary of MIS graduates.)

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 point estimate for the difference between the proportions is

From production line A, a sample of 500 items is selected at random, and it is determined that 30 items are defective. In a sample of 300 items from production process B (which produces identical items to line A), there are 12 defective items. Determine a 95% confidence interval estimate for the difference between the proportions of defectives in the two lines.

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.

A test on world history was given to a group of individuals before and also after a film on the history of the world was presented. The results are given below. We want to determine if the film significantly increased the test scores. (For the following matched samples, let the difference "d" be d = after - before.) a.Give the hypotheses for this problem. b.Compute the test statistic. c.At 95% confidence, test the 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

The following shows the monthly sales in units of six salespersons before and after a bonus plan was introduced. At 95% confidence, determine whether the bonus plan has increased sales significantly. (For the following matched samples, let the difference "d" be: d = after - before.)

Of 200 UTC seniors surveyed, 60 were planning on attending Graduate School. At UTK, 400 seniors were surveyed and 100 indicated that they were planning to attend Graduate School. a.Determine a 95% confidence interval estimate for the difference between the proportion of seniors at the two universities that were planning to attend Graduate School. b.Is there conclusive evidence to prove that the proportion of students from UTC who plan to go to Graduate School is significantly more than those from UTK? Explain.

In order to estimate the difference between the average age of male and female employees at the Young Corporation, the following information was gathered. Develop a 95% confidence interval estimate for the difference between the average age of male and female employees at the Young Corporation.

A manager is thinking of providing, on a regular basis, in-house training for employees preparing for an inventory management certification exam. In the past, some employees received the in-house training before taking the exam, while others did not. Independent random samples taken from the company's records provided the following exam scores for 10 workers who did not receive in-house training and 8 workers who did receive training. (The manager is confident that the distributions of both populations' exam scores are approximately normal.) No Training Training 76 80 80 66 60 71 91 79 73 94 77 74 82 83 68 78 75 86 a. Develop a 95% confidence interval estimate for the difference between the average test scores for the two populations of employees. b. Using $\alpha$ = .05, test for any difference between the average test scores for the two populations of employees.

The results of a recent poll on the preference of voters regarding the presidential candidates are shown below. a.Develop a 90% confidence interval estimate for the difference between the proportion of voters favoring each candidate. b.Does your confidence interval provide conclusive evidence that one of the candidates is favored more? Explain.

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