Question

Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n equals 500 comma x equals 150 comma 95 % confidencen=500, x=150, 95% confidence nothingless than

Answer 1

Answer:

(0.2599,0.3401)                                                

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 500

x = 150

$\hat{p} = \dfrac{x}{n} = \dfrac{150}{500} = 0.3$

Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96$

Putting the values, we get:

$0.3\pm 1.96\sqrt{\dfrac{0.3(1-0.3)}{500}} = 0.3 \pm 0.0401 =(0.2599,0.3401)$

The 95% confidence interval is (0.2599,0.3401).