In a trial of 350 patients who received 10mg doses of a drug

In a trial of 350 patients who received 10-mg doses of a drug daily, 42 reported headache as a side effect. Use this information to complete parts (a) through (d) below. Obtain a point estimate for the population proportion of patients who received 10-mg doses of a drug daily and reported headache as a side effect, p = Q (Round to two decimal places as needed.) Verify that the requirements for constructing a confidence interval about p are satisfied. Are the requirements for constructing a confidence satisfied? Yes, the requirements for constructing a confidence interval are satisfied. No, the requirement that the sample size is no more than 5% of the population is not satisfied. No, the requirement that np(1 - p) is greater than 10 is not satisfied. No, the requirement that each trial be independent is not satisfied. Construct a 90% confidence interval for the population proportion of patients who receive the drug and report headache as a side effect. The 90% confidence interval is (Round to three decimal places as needed.) Interpret the confidence interval. Which statement below best interprets the interval? There is a 90% chance that the true value of p will fall in the interval. There is a 90% chance that the true value of p will not fall in the interval. We are 90% confident that the interval contains the true value of p. We are 90% confident that the interval does not contain the true value of p.

Solution

a)p^=27/100=0.27

b)p*n=0.27*100=27

(1-p)8100=73

both p*n and (1-p)*n are greater than 10 so

yes requirement of constructing confidence interval is satisfied

c) confidence interval

(0.27-1.645*sqrt(0.27*0.73/100), 0.27+1.645*sqrt(0.27*0.73/100))

(0.197 , 0.343)

d) we are 90% confident that interval contain true value of p