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Which of the following 95% confidence intervals would lead us to reject H0:p=0.30in favor of Ha:p≠0.30at 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

Expert verified

(b) (0.19,0.27)

Step by step solution

01

Given information

95% of confidence interval.

H0:p=0.30andHa:p≠0.30

Significant level 5%

02

Explanation

At the nullhypothesis, we test if the proportion is of 0.3, that is: H0:p=0.3

At the alternativehypothesis, we test if the proportion is not equal to 0.3, that is: localid="1650647066210" H1:p≠0.3

We want to reject H0:p=0.3 in favor of H1:p≠0.3 , hence we need an interval that is entirely not equal to 0.3, which is given byoption b.

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