Question

The drug Lipitor is meant to lower cholesterol levels. In a clinical trial of 800 patients, 5% reported headaches.
Construct a 90% confidence interval estimate of the proportion of Lipitor users who will report headaches as a side effect. NO explanation needed or will be reported.

Answer 1

Using the z-distribution, it is found that the 90% confidence interval estimate is given by (0.0373, 0.0627).

What is a confidence interval of proportions?

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

• $\pi$ is the sample proportion.

• z is the critical value.

• n is the sample size.

In this problem, we have a 90% confidence level, hence$\alpha = 0.9$, z is the value of Z that has a p-value of $\frac{1+0.9}{2} = 0.95$, so the critical value is z = 1.645.

The sample size and the estimate are given, respectively, by $n = 800, \pi = 0.05$.

Hence, the bounds of the interval are given by:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.05 - 1.645\sqrt{\frac{0.05(0.95)}{800}} = 0.0373$

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.05 + 1.645\sqrt{\frac{0.05(0.95)}{800}} = 0.0627$

The 90% confidence interval estimate is given by (0.0373, 0.0627).

More can be learned about the z-distribution at https://brainly.com/question/25890103