Question

In a trial of 167 patients who received 10-mg doses of a drug daily, 45 reported headache as a side effect.

(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. (round to two decimal places as needed)

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

Answer 1

a)
`\hat{p} = 0.27`

b) All the conditions are met for constructing a confidence interval.

Explanation:

We are given the following in the question:

Sample size, n = 167

Number of people who had side effects, x = 45

a) point estimate

`\hat{p} = (x)/(n) = (45)/(167) = 0.27`

The 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 0.27

b) Conditions for constructing a confidence interval

1. The data is a random sample from the population of interest.
2. Individual observations can be considered independent.

`n\hat{p}>10\\167* 0.27 = 45.09 > 10\\n(1-\hat{p})>10\\167(1-0.27) = 121.91 > 10`

Thus, all the conditions are met for constructing a confidence interval.