In testing the hypothesis H 0 : D = 5 vs. H 1 : D > 5, two random dependent samp

Question

In testing the hypothesis  H0: D = 5 vs.  H1 :D > 5, two random dependent samples from two normal populations produced the following statistics:nD = 20, xD = 9 and sD = 7.5. What is the rejection region for this test at a 1% significance level?

a. In the right tail of the Z distribution beyond 2.325

b. In the right tail of the t distribution beyond 1.328.

c. In the right tail of the t distribution beyond 2.539.

d. In both tails of the t distribution, beyond -2.861 in the left tail and beyond 2.861 in the right tail.

I need to show my work so I need help understanding how to find the answer and what the answer is. Thanks in advance!

Explanation / Answer

This is a right tailed distribution

Here we will use t distribution.

degree of freedom = 20 - 1 = 19

Critaical value = t0.01,19 = 2.539

Option-C) In the right tail of the t distribution beyond 2.539.

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