91影视

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

$$\begin{gathered} {\stackrel{-}{P}}_c=\frac{x_c}{n_c} \\ =\frac{20}{40} \\ =0.5 \end{gathered}$$

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

$$\begin{gathered} {\stackrel{-}{P}}_s=\frac{x_s}{n_s} \\ =\frac{41}{54} \\ =0.759 \end{gathered}$$

The weighted average role="math" localid="1668666697803" $\left(\stackrel{-}{P}\right)$of P_c and P_s is,

$$\begin{gathered} \stackrel{-}{P}=\frac{x_c+x_s}{n_c+n_s} \\ =\frac{20+41}{40+51} \\ =0.649 \end{gathered}$$

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.

$$\begin{gathered} z=\frac{{\displaystyle \stackrel{-}{p}\stackrel{-}{q}}}{\stackrel{-}{p}\stackrel{-}{q}\left(\frac{1}{n_1}+\frac{1}{n_2}\right)} \\ =\frac{0.5-0.759}{\left(0.649\right)\left(1-0.649\right)\left(\frac{1}{40}+\frac{1}{54}\right)} \\ =\frac{0.25}{0.0996} \\ =-2.60 \end{gathered}$$

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

= 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.

$$\begin{gathered} \left|\frac{\left({{\displaystyle \stackrel{-}{P}}}_s-{{\displaystyle \stackrel{-}{P}}}_c\right)卤Z_{\frac{a}{5}}}{\sqrt{{\displaystyle \frac{{\stackrel{-}{P}}_s\left(1-{\stackrel{-}{P}}_s\right)}{n_s}}+\frac{{\stackrel{-}{P}}_c\left(1-{\stackrel{-}{P}}_c\right)}{n_c}}}\right| \\ =\left(0.759-0.5\right)卤1.93\sqrt{\frac{0.759\left(1-0.759\right)}{54}+\frac{0.5\left(1-0.05\right)}{40}} \end{gathered}$$

= (0.759 - .05) 卤 1.96

= 0.259卤 1.96 (0.09817)

=0.259卤0.1924

= (0.067,0.451)

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.