Answer to Question #143279 in Statistics and Probability for Margaret

Question

A simple random sample of 40 0 individuals provides 100 yes responses . The 95% confidence interval for the population proportion is
1. (0,165 ; 0.335)
2. (0,516 ; 0.535)
3. (0,156 ; 0,335)
4. (0,25; 0,085)
5. (0,2075 ; 0,2925)

Answer 1

$\hat p=\frac{100}{400}=0.4.$

$95\%CI=(\hat p-z_{0.025}\sqrt{\frac{\hat p(1-\hat p)}{n}},\;\hat p+z_{0.025}\sqrt{\frac{\hat p(1-\hat p)}{n}})=$

$=(0.4-1.96\sqrt{\frac{0.4(1-0.4)}{400}},\;0.4+1.96\sqrt{\frac{0.4(1-0.4)}{400}})=$

$=(0.2075,\;0.2925).$

Ans. 5.