Suppose you want to test the claim that $\mu _ { 1 }

Question

Suppose you want to test the claim that $\mu _ { 1 } < \mu _ { 2 }$ Assume the two samples are random and independent. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?
A)There is not sufficient evidence to support the claim μ $\mu _ { 1 } < \mu _ { 2 }$
B)There is sufficient evidence to reject the claim μ $\mu _ { 1 } < \mu _ { 2 } .$
C)There is not sufficient evidence to reject the claim μ $\mu _ { 1 } < \mu _ { 2 }$ .
D)There is sufficient evidence to support the claim μ $\mu _ { 1 } < \mu _ { 2 }$

Quizplus · Accepted Answer

Failing to reject the null hypothesis means there isn't enough evidence to support the alternative hypothesis, which in this case is $\mu _ { 1 } < \mu _ { 2 }$. It does not prove the null hypothesis; it simply indicates insufficient evidence for the alternative.

Suppose You Want to Test the Claim That μ1<μ2\mu _ { 1 } < \mu _ { 2 }μ1​<μ2​

Suppose You Want to Test the Claim That $\mu _ { 1 } < \mu _ { 2 }$