Question

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A drug is used to help prevent blood clots in certain patients. In clinical​ trials, among 4547 patients treated with the​ drug, 114 developed the adverse reaction of nausea. Construct a 99​% confidence interval for the proportion of adverse reactions. ​a) Find the best point estimate of the population proportion p.

Answer 1

The best point estimate of the population proportion p is 0.0251.

The 99​% confidence interval for the proportion of adverse reactions is (0.0191, 0.0311).

Explanation:

In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of
.

In clinical​ trials, among 4547 patients treated with the​ drug, 114 developed the adverse reaction of nausea.

This means that

The best point estimate of the population proportion p is 0.0251.

99% confidence level

So
, z is the value of Z that has a pvalue of
, so
.

The lower limit of this interval is:

The upper limit of this interval is:

The 99​% confidence interval for the proportion of adverse reactions is (0.0191, 0.0311).