# Four Calculus Problems

1. Efficacy of a drug. Seventy-five (75) people with hypertension were given a new drug for the treatment of their condition. Blood pressure was lowered sufficiently to reduce the risk of serious outcomes in 20 of the 75 patients.(A) In what proportion of the sample did the drug work? (Calculate P).(2 points)(B) Calculate a 95% confidence interval for the proportion. Show all work, and interpret your findings. (Check to see if you can use a normal approximation before calculating the confidence interval.) (4 points)(C) How large a sample would be needed to reduce the margin of error to .05? (4 points)2. Determine the sample size needed to calculate a 95% confidence interval for a proportion with a margin or error of 10%. (4 points)3. Survival in pediatric cancer cases. An oncologist treats 40 cases of kidney cancer. In the past, this disease had a five-year survival rate of 1 in 5 (20%). In the 40 patients the oncologist treats, 16 survive for at least five years. Test to see whether this treatment is associated with a significantly higher survival than in the past. (Let a = .01, two-sided.) List all hypothesis testing steps. Was survival improved significantly? (8 points)4. Cancers in insulation workers. There were 26 cancer deaths in a cohort of 556 insulation workers. Based on studies in comparably populations, only 14.4 cancer deaths were expected.(A) What was the observed cancer morality proportion in the group?(2 points)(B) What was the expected cancer mortality proportion in the group under H0? (2 points)(C) Test whether the observed mortality proportion is significantly greater than expected. Use a two-sided test at a = .01 level. List all hypothesis testing steps (including H0 and Ha), and show all work. (8 points)