A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. A 95% confidence interval for the difference between the population means is (1.4, 8.7). If the hypothesis test is based on the same samples, which of the following do you know for sure:
A: The hypothesis $\mu _ { 1 } = \mu _ { 2 }$ would be rejected at the $5 \%$ level of significance.
B: The hypothesis $\mu _ { 1 } = \mu _ { 2 }$ would be rejected at the $10 \%$ level of significance.
$C$ : The hypothesis $\mu _ { 1 } = \mu _ { 2 }$ would be rejected at the $1 \%$ level of significance.

A) A and C
B) A only
C) A, B, and C
D) A and B

Question

A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. A 95% confidence interval for the difference between the population means is (1.4, 8.7). If the hypothesis test is based on the same samples, which of the following do you know for sure: 
A: The hypothesis $\mu _ { 1 } = \mu _ { 2 }$ would be rejected at the $5 \%$ level of significance.
B: The hypothesis $\mu _ { 1 } = \mu _ { 2 }$ would be rejected at the $10 \%$ level of significance.
$C$ : The hypothesis $\mu _ { 1 } = \mu _ { 2 }$ would be rejected at the $1 \%$ level of significance.

A) A and C
B) A only
C) A, B, and C
D) A and B

Quizplus · Accepted Answer

The 95% confidence interval (1.4, 8.7) does not include 0, indicating that the null hypothesis $\mu_1 = \mu_2$ would be rejected at the 5% significance level. Since the interval is entirely above 0, it would also be rejected at the 10% level, but not necessarily at the 1% level.

A Hypothesis Test Is to Be Performed to Test the Equality