Answer:
The 90% confidence interval of the population proportion is (0.43, 0.56).
Step-by-step explanation:
The (1 - α)% confidence interval for population proportion p is:
[tex]CI=\hat p\pm z_{\alpha/2}\ \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information provided is:
X = 74
n = 150
Confidence level = 90%
Compute the value of sample proportion as follows:
[tex]\hat p=\frac{X}{n}=\frac{74}{150}=0.493[/tex]
Compute the critical value of z for 90% confidence level as follows:
[tex]z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645[/tex]
*Use a z-table.
Compute the 90% confidence interval of the population proportion as follows:
[tex]CI=\hat p\pm z_{\alpha/2}\ \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]=0.493\pm 1.645\times \sqrt{\frac{0.493(1-0.493)}{150}}\\\\=0.493\pm 0.0672\\\\=(0.4258,\ 0.5602)\\\\\approx (0.43,\ 0.56)[/tex]
Thus, the 90% confidence interval of the population proportion is (0.43, 0.56).
