Question

In a trial of 300 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.

​(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.

ModifyingAbove p with caretpequals=nothing ​(Round to two decimal places as​ needed.)

Are the requirements for constructing a confidence​ satisfied?

A.

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

B.

​No, the requirement that each trial be independent is not satisfied.

C.​No, the requirement that

n ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesisnp1−p is greater than 10 is not satisfied.

D.

​No, the requirement that the sample size is no more than​ 5% of the population is not satisfied.

​(c) Construct a

9999​%

confidence interval for the population proportion of patients who receive the drug and report headache as a side effect.

The

9999​%

confidence interval is

​(nothing​,nothing​).

​(Round to three decimal places as​ needed.)

​(d) Interpret the confidence interval. Which statement below best interprets the​ interval?

A.We are

9999​%

confident that the interval contains the true value of p.

B.There is a

9999​%

chance that the true value of p will not fall in the interval.

C.We are

9999​%

confident that the interval does not contain the true value of p.of p.

D.There is a

9999​%

chance that the true value of p will fall in the interval.

Answer 1

The statistical software output for this problem is:

From above output:

a) p = 0.14

b) Yes, the requirements for constructing a confidence interval are satisfied.

c) 99% confidence interval:

(0.088, 0.192)

d) Option A is correct.