Answer:
The minimum sample size required is 97.
Step-by-step explanation:
The (1 - α)% confidence interval for the population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error for this confidence interval is:
[tex]MOE=z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information provided is:
[tex]\hat p=0.20\\MOE=0.08\\\text{Confidence level}=95\%[/tex]
The critical value of z for 95% confidence level is, z = 1.96.
Compute the minimum sample size required as follows:
[tex]MOE=z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\cdot\sqrt{\hat p(1-\hat p)}}{MOE}]^{2}\\\\=[\frac{1.96\times \sqrt{0.20(1-0.20)}}{0.08}]^{2}\\\\=96.04\\\\\approx 97[/tex]
Thus, the minimum sample size required is 97.
