91影视

Let N denotes the business were member of the Governor鈥檚 Council, i.e. $N=251$

Let x denotes the number of the council admitted that they had employees, i.e. $x=50$

The sample size is $n=72$

Since, the proportion of all business were member of the Governor鈥檚 Council business members who have employee with substance abuse problems is,

$\hat{p}=\frac{x}{n}$

Therefore,

$\begin{array}{rcl}\hat{p}& =& \frac{50}{72}\\ & =& 0.6944\\ & & \end{array}$

The 95% confidence intervals obtained by using the following formula:

$\begin{array}{rcl}\hat{p}卤2\left(\sqrt{\frac{\hat{p}\left(1-\hat{p}\right)}{n}}脳\sqrt{\frac{N-n}{N}}\right)& =& 0.6944卤2\left(\sqrt{\frac{0.6944\left(1-0.6944\right)}{72}}脳\sqrt{\frac{251-72}{251}}\right)\\ & =& 0.6944卤2\left(\sqrt{\frac{0.6944脳0.3056}{72}}脳\sqrt{\frac{179}{251}}\right)\\ & =& 0.6944卤2\left(\sqrt{0.0029473}脳\sqrt{0.713147}\right)\\ & =& 0.6944卤0.0916\\ & =& \left(0.6028,0.7860\right)\\ & & \end{array}$

Hence, it is 95% confident that, the true proportion of all New Jersey Governor Council business members who have employee with substance abuse problem lies in between 0.6028 and 0.7860.