4.14 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 S S F S S S F F S S

a. What is the value of the sample proportion of successes?

b. Replace each S with a 1 and each F with a 0. Then calculate x for this numerically coded sample.
How does x compare to p ^ ?

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 p ^ 5 .80 for the entire sample of 25 patients?