91Ó°ÊÓ

The given values are,

$$\begin{gathered} x_1=446, \\ {n}_1=537, \\ {x}_2=307, \\ {n}_2=495, \\ \mathrm{Î\pm }=0.01 \end{gathered}$$

The formula for ${\tilde{p}}_1$is given by,

${\tilde{p}}_1=\frac{x_1}{n_1}$

The formula for ${\tilde{p}}_2$is given by,

${\tilde{p}}_2=\frac{x_2}{n_2}$

The formula for $z$is given by,

$z=\frac{{\tilde{p}}_1-{\tilde{p}}_2}{\sqrt{{\tilde{p}}_p\left(1-{\tilde{p}}_p\right)}\sqrt{\frac{1}{m_1}+\frac{\mathrm{Γ}}{m_2}}}$

The formula for ${\tilde{p}}_p$is given by,

${\tilde{p}}_p=\frac{x_1+x_2}{n_1+n_2}$

The values $x_1,\left(n_1-x_1\right),x_2$, and $\left(n_2-x_2\right)$are all greater than 5 .

The value of ${\tilde{p}}_1$is calculated as,

$$\begin{gathered} {\tilde{p}}_1=\frac{x_1}{n_1} \\ =\frac{446}{537} \\ =0.83 \end{gathered}$$

The value of ${\tilde{p}}_2$is calculated as,

$$\begin{gathered} {\tilde{p}}_2=\frac{x_2}{n_2} \\ =\frac{307}{495} \\ =0.62 \end{gathered}$$

The value of ${\tilde{p}}_p$is calculated as,

$$\begin{gathered} {\tilde{p}}_p=\frac{x_1+x_2}{n_1+n_2} \\ =\frac{446+307}{537+495} \\ =0.73 \end{gathered}$$

The value of $z$is calculated as,

$z=\frac{{\tilde{p}}_1-{\tilde{p}}_2}{\sqrt{\tilde{p}\left(1-{\tilde{p}}_p\right)}\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

$$\begin{gathered} =\frac{0.83-0.62}{\sqrt{0.73(1-0.73)}\left(\sqrt{\frac{1}{537}+\frac{1}{495}}\right)} \\ =7.698 \end{gathered}$$

The value of $z$- value.

$z\_\left\{a\right\}=z\_\{0.01\}=2.326$

Calculate $z$- value $(=7.698)$is greater than the critical value

$(=2.326).$

We concluded that the data suggest that women prefer ballistic fingerprinting over men at the$1\%$ level of significance.

As a result, at a 1% level of significance, the data suggest that women prefer ballistic fingerprinting over men.