Chapter 4.1, Problem 14E

Suppose that 10 patients with meningitis received treatment with large doses of penicillin. Three days later, temperatures were recorded, and the treatment was considered successful if there had been a reduction in a patient’s temperature. Denoting success by S and failure by F, the 10 observations are

1. a. What is the value of the sample proportion of successes?
2. b. Replace each S with a 1 and each F with a 0. Then calculate $\bar{x}$ for this numerically coded sample. How does $\bar{x}$ compare to $\hat{p}$?
3. c. Suppose that it is decided to include 15 more patients in the study. How many of these would have to be S’s to give $\hat{p}=0.80$ for the entire sample of 25 patients?