91影视

The sample proportion for the client-flow website is obtained below.

$\begin{array}{l}{\stackrel{炉}{P}}_c=\frac{x_c}{n_c}\\ =\frac{20}{40}\\ =0.5\end{array}$

The sample proportion for the serve-flow website is obtained below.

$\begin{array}{l}{\stackrel{炉}{P}}_s=\frac{x_s}{n_s}\\ =\frac{41}{54}\\ =0.759\end{array}$

The weighted average $\left(\overline{P}\right)$ of P_c and P_s is,

$\begin{array}{l}\stackrel{炉}{P}=\frac{x_c+x_s}{n_c+n_s}\\ =\frac{20+41}{40+54}\\ =\frac{61}{94}\\ =0.649\end{array}$

Null hypothesis:

H_0: P_S鈥� P_c= 0

The client-flow website is not more likely to be vulnerable to a special attack than a serve-flow website.

Alternative hypothesis:

H_a= P_s- P_c< 0

The client-flow website is more likely to be vulnerable to a special attack than a serve-flow website.

$\begin{array}{l}z=\frac{{\stackrel{炉}{p}}_1{\stackrel{炉}{q}}_1}{\stackrel{炉}{p}\stackrel{炉}{q}[\frac{1}{n_1}+\frac{1}{n_2}]}\\ =\frac{0.5鈭�0.759}{\left(0.649\left)\right(1鈭�0.649\right)(\frac{1}{40}+\frac{1}{54})}\\ =\frac{鈭�0.25*}{0.0996}\\ =鈭�2.60\end{array}$

Thus, the test statistic is -2.60.

The critical value is obtained below.

Here, the test is two-tailed, and the significance level is 伪 = 0.05.

The confidence coefficient is 0.95.

So,

(1-伪)=0.95

螒=0.05

$\frac{伪}{2}$= 0.025

From appendix D, table 2, the critical value for the two-tailed test with 伪 = 0.05 is$z_{\frac{a}{2}}$_(-0.025)= 1.96.

Here, the test statistic falls in the rejection region.

So, the null hypothesis was rejected.

Determine how much a client-flow website is more likely to be vulnerable to a special attack than a server-flow website.

$$\begin{gathered} =\left[\begin{array}{c}({\stackrel{炉}{P}}_s鈭�{\stackrel{炉}{P}}_c)卤z_{\frac{a}{5}}\\ \sqrt{\frac{{\stackrel{炉}{p}}_s(1鈭�{\stackrel{炉}{P}}_s)}{n_5}+\frac{{\stackrel{炉}{P}}_c(1鈭�{\stackrel{炉}{P}}_c)}{n_c}}\end{array}\right] \\ =(0.759-.05)卤1.96\sqrt{\frac{0.759(1鈭�0.759)}{54}+\frac{0.5(1鈭�0.05)}{40}} \\ =0.259卤1.96(0.09817) \\ =0.259卤0.1924 \\ =(0.067,0.451) \end{gathered}$$

So, 95% confidence interval is (0.067,0.451).

There is 95% confidence that a client-flow website is more likely to be vulnerable to a special attack than a server-flow website is, from 0.067 to 0.451.