Question

Which of the following 95% confidence intervals would lead us to reject $H0:p=0.30$in favor of $Ha:p\ne 0.30$at the 5% significance level?

(a) (0.29, 0.38) (c) (0.27, 0.31) (e) None of these

(b) (0.19, 0.27) (d) (0.24, 0.30)

Short answer

(b) (0.19,0.27)

Step-by-step solution

Given information

95% of confidence interval.

$H_0:p=0.30$and$Ha:p\ne 0.30$

Significant level 5%

Explanation

At the nullhypothesis, we test if the proportion is of 0.3, that is: $H_0:p=0.3$

At the alternativehypothesis, we test if the proportion is not equal to 0.3, that is: localid="1650647066210" $H_1:p\ne 0.3$

We want to reject $H_0:p=0.3$ in favor of $H_1:p\ne 0.3$ , hence we need an interval that is entirely not equal to 0.3, which is given byoption b.