Question

n a trial of 125 patients who received​ 10-mg doses of a drug​ daily, 45 reported headache as a side effect. Use this information to complete parts​ (a) through​ (d) below. ​

(a) 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= ​(Round to two decimal places as​ needed.)

​(b) Verify that the requirements for constructing a confidence interval about p are satisfied. Are the requirements for constructing a confidence​ satisfied?

A.​Yes, the requirements for constructing a confidence interval are satisfied. B. ​No, the requirement that np1−p is greater than 10 is not satisfied. C. ​No, the requirement that the sample size is no more than​ 5% of the population is not satisfied. D. No, the requirement that each trial be independent is not satisfied.

​(c) 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.)

​(d) Interpret the confidence interval. Which statement below best interprets the​ interval? A.We are 90​% confident that the interval does not contain the true value of p. B.There is a 90​% chance that the true value of p will not fall in the interval. C. We are 90​% confident that the interval contains the true value of p. D. There is a 90​% chance that the true value of p will fall in the interval.

Answer 1

(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 is,

p = 45 / 125 = 0.36

(b)

np(1-p) = 125 * 0.36 * (1 - 0.36) = 28.8

Since np(1-p) > 10, the sample size is large enough to construct the confidence interval.

It can be assumed that the sample size is no more than​ 5% of the population and the trials are independent.

A.​Yes, the requirements for constructing a confidence interval are satisfied.

(c)

Standard error of sample proportion, SE =

= 0.04293251

Z value for 90​% confidence interval is 1.645

90​% confidence interval for the population proportion of patients who receive the drug and report headache as a side effect is,

(0.36 - 1.645 * 0.04293251 ,  0.36 + 1.645 * 0.04293251)

(0.289 ,  0.431)

(d)

The interpretation of the confidence interval is,

C. We are 90​% confident that the interval contains the true value of p.