Test the claim below about the mean of the difference of two

Test the claim below about the mean of the difference of two populations. Use a t-test for dependent, random samples at the given level f signifance with the given statistics.

Claim: ud=0, alpha=0.01. Statistics: d=3.8, sd=8.41, n=9

a) is the test right tailed, left tailed, or two tailed?

b) should the null hypothesis be rejected?

Solution

A.

TWO TAILED. As we can see, the claim used an = sign. Thus, it is two tailed.

B.

As for a 2 sample t test,

t = (d - ud) * sqrt(n) / sd

Then

t = 1.3555

As df = n - 1 = 8, then using table or technology,

tcrit = 3.355387331

As t < tcrit, WE FAIL TO REJECT THE NULL HYPOTHESIS.

So, the answer for part B IS NO. [ANSWER, PART B]