Question

A random sample of 225 items from a population results in 60% possessing a given characteristic. Using this information, the researcher constructs a 99% confidence interval to estimate the population proportion. The resulting confidence interval is _______.

Answer 1

Answer: $(0.52,\ 0.68)$

Step-by-step explanation:

The formula for a $\alpha$- level confidence interval for the population proportion:-

$p\pm z_{\alpha/2}\times\sqrt{\dfrac{p(1-p)}{n}}$

Given : n = 225 ; p = 0.60 ; $\alpha= 1-0.99=0.01$

By using the given information , the confidence interval for the population proportion:-

$0.6\pm z_{0.005}\times\sqrt{\dfrac{0.6(1-0.6)}{225}}\\\\=0.6\pm(2.576)(0.0327)\\\\=0.6\pm0.08\\\\=0.6-0.08,\ 0.6+0.08\\\\=(0.52,\ 0.68)$

Hence, the resulting confidence interval is $(0.52,\ 0.68)$ .