Question

A random sample of 205 college students was asked if they believe that places could be haunted, and 65 responded yes. estimate the true proportion of college students who believe in the possibility of haunted places with 99 % confidence.

Answer 1

Answer:

The 99% confidence interval is given below:

$\hat{p} \pm z_{\frac{0.01}{2}}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

Where:

$\hat{p}=\frac{65}{205}=0.3171$

$z_{\frac{0.01}{2}}=2.576$ is the critical value at 0.01 significance level

$n=205$

$\therefore 0.3171 \pm 2.576\sqrt{\frac{0.3171(1-0.3171)}{205} }$

       $0.3171 \pm 0.0837$

       $\left(0.23, 0.40 \right)$ rounded to two decimal places

Therefore, the estimate of the true proportion of college students who believe in the possibility of haunted places with 99% confidence is (0.23,0.40).