Question

A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94. The treatment is expected to increase scores and the sample mean shows an increase. Which of the following is the correct decision for a hypothesis test using α = .05.
- Reject the null hypothesis with either a one-tailed or a two-tailed test
- Fail to reject the null hypothesis with a one-tailed test but reject with two tails
- Reject the null hypothesis with a one-tailed test but fail to reject with two tails
- Fail to reject the null hypothesis with either a one-tailed or a two-tailed test

Answer 1

Answer:

Option 3) We reject the null hypothesis with one tail test and accept the null hypothesis with two tail test.

Step-by-step explanation:

We are given the following information:

n = 16

$t_{statistic} = 1.94$

$\alpha = 0.05$

Now,

Right One-tail Test

$t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753$

$t_{stat} > t_{critical}$

We reject the null hypothesis in this case.

Two-tail Test

Now, $t_{critical} \text{ at 0.05 level of significance, 9 degree of freedom } = \pm 2.131$

$-2.131 < t_{stat} < 2.131$

We accept the null hypothesis in this case.

Option 3) We reject the null hypothesis with one tail test and accept the null hypothesis with two tail test.