SOLVE THE FOLLOWING EXERCISES. THEY MUST SHOW IN EACH ONE THE COMPUTERS MADE AND END WITH A CONCLUSION TO WHAT IS POSED. I. Proof of a claim about a proportion:

1. The municipal government of a city uses two methods to register properties. 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. In a sample of 75 from method II, 10 errors were found. Probably at the .15 significance level the personal method produces fewer errors than the mail-in method.

2. A pharmaceutical firm is testing two components for regular pressure. The components were administered to two groups. In group I, 71 out of 100 patients managed to control their 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. Proof of a claim about a mean: known

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 a 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 the .05 significance level if there is a salary difference between the two cities.

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

III. Assertion test about a mean: unknown

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