SOLVE THE FOLLOWING EXERCISES. IN EACH ONE YOU MUST SHOW THE COMPUTATIONS MADE AND FINISH WITH A CONCLUSION TO THE QUESTION. I. Proof of an assertion regarding a proportion: 1. The municipal government of a city uses two methods to register property. The first requires the owner to go in person. The second allows registration by mail. A sample of 50 was taken from method I and 5 errors were found. A sample of 75 from method II found 10 errors. Test at a significance level of .15 that the in-person method produces fewer errors than the mail-in method.

2. A pharmaceutical firm is testing two components to regulate pressure. The components were administered to two groups. In group I, 71 of 100 patients were able to control their blood pressure. In group II, 58 of 90 patients achieved the same. The company wants to prove at a significance level of .05 that there is no difference in the efficacy of the two drugs.

II. Testing an assertion with respect to a known mean: 1. A firm wants to determine whether the hourly wages of two employees are the same or different. A sample of 200 was taken in city I and reflected a mean of $8.95, with standard deviation of .40. In city II a sample of 175 was taken with a mean of $9.10 with a standard deviation of .60. The firm wants to determine at .05 significance whether there is a wage differential between the two cities.

2. Two research laboratories produced a drug for the relief of arthritis. The drug from lab #1 was tested on 90 patients with an average of 8.5 hours of relief and standard deviation of 1.8 hours. Lab drug #2 was tested in 80 patients and produced 7.9 hours of relief with standard deviation of 2.1 hours. At a significance level of .05 I determined if the lab #1 drug provides longer relief time than lab #2.

III. assertion test with respect to a mean: unknown. 1. In a promotion contest in Ireland, the ages of unsuccessful and successful applicants who were successful in obtaining promotion were studied. For unsuccessful applicants a sample of 23 was used, which reflected a mean age of 47 and standard deviation of 7.2. The sample of successful applicants had a mean of 43.9, with a standard deviation of 5.9, in 30 cases analyzed. Use .05 level of significance to test the assertion that the unsuccessful applicants come from a larger mean population than the successful applicants.