A random sample of 75 printers discovered that 25 of them were being used in small businesses . Find the 99% limit for the population proportion of printers that are used in
Small businesses.
A) $0.193

Question

A random sample of 75 printers discovered that 25 of them were being used in small businesses . Find the 99% limit for the population proportion of printers that are used in
Small businesses. 
A) $0.193 < p < 0.473$
B) $0.287 < p < 0.380$
C) $0.066 < p < 0.601$
D) $0.207 < p < 0.460$

Quizplus · Accepted Answer

The 99% confidence interval for a proportion is calculated using the formula $\hat{p} \pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where $\hat{p}$ is the sample proportion, $z$ is the z-score corresponding to the confidence level (for 99% confidence, $z \approx 2.576$), and $n$ is the sample size. Here, $\hat{p} = \frac{25}{75} = \frac{1}{3}$ and $n = 75$. Plugging these values into the formula gives the interval $0.193 < p < 0.473$, which matches choice A.

A Random Sample of 75 Printers Discovered That 25 of Them