Answer:
The sample size required is, n = 502.
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\cdot (1-\hat p)}{n}}[/tex]
The margin of error is:
[tex]MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}[/tex]
Assume that 50% of the people would support this political candidate.
The margin of error is, MOE = 0.05.
The critical value of z for 97.5% confidence level is:
z = 2.24
Compute the sample size as follows:
[tex]MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}[/tex]
[tex]=[\frac{2.24\times \sqrt{0.50(1-0.50)}}{0.05}]^{2}\\\\=501.76\\\\\approx 502[/tex]
Thus, the sample size required is, n = 502.
