In a trial of 180 patients who received 10-mg doses of a drug daily, 27 reported

Question

In a trial of 180 patients who received 10-mg doses of a drug daily, 27 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. (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 95% confidence interval for the population proportion of patients who receive the drug and report headache as a side effect. The 95% confidence interval is (Round to three decimal places as needed.) Interpret the confidence interval. Which statement below best interprets the interval? There is a 95% chance that the true value of p will fall in the interval. We are 95% confident that the interval does not contain the true value of p. We are 95% confident that the interval contains the true value of p. There is a 95% chance that the true value of p will not fall in the interval.

Explanation / Answer

a) point estimate =phat=27/180=0.15

b) nphat=180*0.15=27>10

and np(1-p)=22.95>10

option A is correct

c)here std error =(p(1-p)/n)1/2=0.0266

for 95% CI, z=1.96

hence confidence interval =mean +/- z*std error =(0.098 ; 0.202)

d)option A is correct

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