Question

A significance test for comparing two means gave t = -1.97 with 10 degrees of freedom. Can you reject the null hypothesis that the M’s are equal vs the one-sided alternative at the 5% significance level?

Step 1: True or false: we can reject in favor of the two-sided alternative at the 5% level

Step 2: True or false we can reject the null hypothesis in favor of M1 < M2

Answer 1

From the given information,

Test statistic= -1.97

Critical value= -1.81

As test statistic < critical value

Hence,

Yes, We have to reject null hypothesis that the M’s are equal vs the one-sided alternative at the 5% significance level.

Step 1. For two sided alternative,

Test statistic > critical value (-2.23)

Hence, we can not reject null hypothesis.

Hence, This statement is false.

Step 2. From the above information,

We have to reject null hypothesis for one-sided alternative.

Hence, This statement is true.

Thank you.