Q. 60 - The Practice of Statistics for AP

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)

Step-by-Step Solution

Answer

(b) (0.19,0.27)

Step 1: Given information

95% of confidence interval.

$H_0 :p = 0.30$ and$Ha :p \ne 0.30$

Significant level 5%

Step 2: Explanation

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

At the alternative hypothesis, we test if the proportion is not equal to 0.3, that is: $H_1:p \ne 0.3$

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 by option b.