Answer:
The reasonable range for the population mean is (61%, 75%).
Step-by-step explanation:
The interval estimate of a population parameter is an interval of values that consist of the values within which the true value of the parameter lies with a certain probability.
The mean of the sampling distribution of sample proportion is, [tex]\hat p[/tex].
One of the best interval estimate of population proportion is the 95% confidence interval for proportion,
[tex]CI=\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Given:
n = 150
[tex]\hat p[/tex] = 0.68
The critical value of z for 95% confidence level is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
Compute the 95% confidence interval for proportion as follows:
[tex]CI=\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]=0.68\pm1.96\sqrt{\frac{0.68(1-0.68)}{150}}\\\\=0.68\pm 0.0747\\\\=(0.6053, 0.7547)\\\\\approx (0.61, 0.75)[/tex]
Thus, the reasonable range for the population mean is (61%, 75%).
