Question

Ballistic Fingerprinting. Guns make unique markings on bullets they fire and their shell casings. These markings are called holistic fingerprints. An ABCNEWS Podl examined the opinions of Americans on the enactment of a law "...that would require every gun sold in the United States to be test-fired first, so law enforcement would have its fingerprint in case it were ever used in a crime."

level, do the data provide sufficient evidence to conclude that women tend to favor ballistic fingerprinting more than men'?

Short answer

At $1\%$level of significance, the data suggest that women find to favor ballistic fingerprinting more than men,

Step-by-step solution

Given Information

The given values are,

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

Explanation

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,

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

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.