Answer:
The 95% confidence interval for the true population proportion is (0.27, 0.33).
Step-by-step explanation:
The (1 - α)% confidence interval for population proportion of is:
[tex]CI=\hat p \pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information given is:
[tex]\hat p=0.30\\n=765\\\text{Confidence level}=95\%[/tex]
The critical value of z for 95% confidence level is, 1.96.
Compute the 95% confidence interval for the true population proportion as follows:
[tex]CI=\hat p \pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]=0.30\pm 1.96\times\sqrt{\frac{0.30(1-0.30)}{765}}\\\\=0.30\pm 0.0325\\\\=(0.2675, 0.3325)\\\\\approx (0.27, 0.33)[/tex]
Thus, the 95% confidence interval for the true population proportion is (0.27, 0.33).
