Answer:
The number of citizens that should be included in the sample is 151.
Step-by-step explanation:
The (1 - α)% confidence interval for population mean is:
[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
The margin of error for this interval is:
[tex]MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]MOE=4\\\sigma = 25\\[/tex]
Confidence level = 95%
α = 5%
Compute the critical value of z for α = 5% as follows:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
*Use a z-table.
Compute the sample size required as follows:
[tex]MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\times \sigma}{MOE} ]^{2}[/tex]
[tex]=[\frac{1.96\times 25}{4}]^{2}\\\\=150.0625\\\\\approx 151[/tex]
Thus, the number of citizens that should be included in the sample is 151.
