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 4105 patients treated with the drug, 111 developed the adverse reaction of
nausea. construct a 90% confidence interval for the proportion of adverse reactions.
a) find the best point estimate of the population proportion p.
(round to three decimal places as needed.)

Explanation:

Step1: Recall the formula for the best point estimate of a population proportion

The best point estimate of a population proportion \(p\) is the sample proportion \(\hat{p}\). The formula for the sample proportion is \(\hat{p}=\frac{x}{n}\), where \(x\) is the number of successes (in this case, the number of patients who developed adverse reactions) and \(n\) is the sample size.

Step2: Identify the values of \(x\) and \(n\)

From the problem, \(x = 111\) (the number of patients with adverse reactions) and \(n=4105\) (the total number of patients treated with the drug).

Step3: Calculate the sample proportion \(\hat{p}\)

Substitute \(x = 111\) and \(n = 4105\) into the formula \(\hat{p}=\frac{x}{n}\). So, \(\hat{p}=\frac{111}{4105}\approx0.027\)

Answer:

\(0.027\)