Answer:
(0.2599,0.3401)
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 500
x = 150
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{150}{500} = 0.3[/tex]
Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96[/tex]
Putting the values, we get:
[tex]0.3\pm 1.96\sqrt{\dfrac{0.3(1-0.3)}{500}} = 0.3 \pm 0.0401 =(0.2599,0.3401)[/tex]
The 95% confidence interval is (0.2599,0.3401).
