In a trial of 400 patients who received 10-mg doses of a drug daily, 48 reported

Question

In a trial of 400 patients who received 10-mg doses of a drug daily, 48 reported headache as a side effect. Use this information (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. (b) Varity 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 the sample size is no more than 5% of the population is not satisfied. C. No. the requirement that each trial be independent is not satisfied. D. No. the requirement that np(1 - p) is greater than 10 is not satisfied (C) Construct a 90% confidence interval for the population of parents who received the drug and report headache as a side effect (d) Interpret the confidence interval, Which statement below best interprets the interval? A. There is a 90% chance that the true value of p will fall in the interval

Explanation / Answer

Part (a)

Point estimate of population proportion = sample proportion = 48/400 = 0.12 ANSWER

Part (b)

Methodology for constructing CI is based on the Normal approximation to Binomial probability.

Requisite conditions for this approximation are np > 10 and np(1 - p) > 10/

In the given problem, np = 400x0.12 = 48 > 10 and np(1 - p) = 48x0.88 = 42.24 > 10.

Since both conditions are satisfied, answer is option (a) ANSWER

Part (c)

90% CI for population proportion is: p ± Z0.05xsqrt{p(1 - p)/n} = 0.12 ± 1.645 x sqrt(0.000264)

= 0.12 ± 0.027 ANSWER

Part (d)

Interpretation of CI: there is 90% chance that the true population proportion will lie between

0.093 and 0.147. ANSWER

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