Solve the problem.
-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, B, and C
B) A only
C) A and C
D) A and B

Question

Solve the problem.
-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, B, and C
B) A only
C) A and C
D) A and B

Quizplus · Accepted Answer

Since the 95% confidence interval for the difference between the population means does not include 0, we can reject the null hypothesis $\mu _ { 1 } = \mu _ { 2 }$ at the 5% level of significance. This also implies rejection at any higher level of significance, such as 10%, but not necessarily at a lower level like 1%.

Solve the Problem μ1=μ2\mu _ { 1 } = \mu _ { 2 }μ1​=μ2​

Solve the Problem $\mu _ { 1 } = \mu _ { 2 }$