In a trial of 350 partients who recieved 10mg doses of a dru

In a trial of 350 partients who recieved 10-mg doses of a drug daily, 49 reported headache as a side effect. Construct a 90% confidence interval for the population proportion of patients who recieve the drug and report headache as a side effect. The 90% confidence interval is (______, ______) round answer three decimal places as needed.

Interpret the confidence interval. Which statement below best interprets the interval?

a. we are 90% confident that the interval contains the true value of p.

b. there is a 90% chance that the true value of p will fall in the interval.

c. there is a 90% chance that the true value of p will not fall in the interval.

d. we are 90% confident that the interval does not contain the true value of p.

Solution

p=49/350 = 0.14

Given a=1-0.9=0.1, Z(0.05) = 1.645 (from standard normal table)

So the lower bound is

p- Z*sqrt(p*(1-p)/n) = 0.14 -1.645*sqrt(0.14*(1-0.14)/350) =0.109

So the upper bound is

p+ Z*sqrt(p*(1-p)/n) = 0.14 +1.645*sqrt(0.14*(1-0.14)/350) =0.171

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a. we are 90% confident that the interval contains the true value of p.