Question

Repatha® (evolocumab) is used to reduce the risk of heart attack or stroke in adults with heart disease or as a treatment to lower high LDL cholesterol. One of the possible side effects of Repatha is that it can lead to high blood sugar (glucose) levels. The manufacturer of Repatha wants to estimate the true proportion of all patients who will experience high blood sugar levels as a result of using Repatha. A random sample of 400 patients treated with Repatha was taken. Of these 400 patients, 120 were found to have high blood sugar levels.

Construct a 93% confidence interval estimate of the proportion of all Repatha users who will experience high blood sugar levels when being treated with Repatha. Use only the appropriate formula and/or statistical table in your textbook to answer this question. Negative values should be indicated by a minus sign. Report your answers to 2 decimal places, using conventional rounding rules.

Answer:____ ≤ p/σ/n/μ/π/x-bar/s ≤_______

Using the sample proportion as a planning value, what sample size would be required to estimate π to within.03, with 93% confidence?

Answer:  

Answer 1

a) $\widehat \pi$ = 120/400 = 0.3

At 93% confidence interval the critical value is z_0.035 = 1.81

The 93% confidence interval for $\pi$ is

$\widehat \pi$ +/- z_0.035 * sqrt( $\widehat \pi$ (1 - $\widehat \pi$ )/n)

= 0.3 +/- 1.81 * sqrt(0.3 * 0.7/400)

= 0.3 +/- 0.04

= 0.26, 0.34

0.26 < $\pi$ < 0.34

b) Margin of error = 0.03

or, z_0.035 * sqrt( $\pi$ (1 - $\pi$ )/n) = 0.03

or, 1.81 * sqrt(0.3 * 0.7/n) = 0.03

or, n = (1.81 * sqrt(0.3 * 0.7)/0.03)^2

or, n = 765