Answer:
The minimum sample size required is 1449.
Step-by-step explanation:
The (1 - α) % confidence interval for population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error in this interval is:
[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Given:
[tex]\hat p = p = 0.38\\MOE=2.5\%\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
*Use the z-table for the critical value.
Compute the value of n as follows:
[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.38\times(1-0.38)}{0.0025^{2}}\\=1448.129536\\\approx1449[/tex]
Thus, the minimum sample size required is 1449.
