ANSWER:
595
STEP-BY-STEP EXPLANATION:
Given:
Proportion (p) = 0.45
Margin of error (E) = 0.04
At 95% confidence level the z is:
[tex]\begin{gathered} \alpha=1-95\% \\ \\ \alpha=1-0.95=0.05 \\ \\ \alpha\text{/2}=\frac{0.05}{2}=0.025 \\ \\ \text{ The corresponding value of Z would be:} \\ \\ Z_{\alpha\text{/2}}=1.96 \end{gathered}[/tex]We can calculate the value of the sample by the following formula:
[tex]\begin{gathered} E=Z_{\alpha\text{/2}}\cdot\sqrt{\frac{p\cdot(1-p)}{n}} \\ \\ \text{ We replacing:} \\ \\ 0.04=1.96\cdot \sqrt{\frac{0.45\cdot \left(1-0.45\right)}{n}} \\ \\ \sqrt{\frac{0.45\left(1-0.45\right)}{n}}=\frac{0.04}{1.96} \\ \\ \frac{0.45\left(1-0.45\right)}{n}=\left(\:\frac{0.04}{1.96}\right)^2 \\ \\ \frac{1}{n}=\frac{\left(\:\frac{0.04}{1.96}\right)^2}{0.45\left(1-0.45\right)} \\ \\ n=\frac{0.45\left(1-0.45\right)}{\left(\:\frac{0.04}{1.96}\right)^2} \\ \\ n=594.2475\cong595 \end{gathered}[/tex]The sample size is 595
