Question

A researcher conducts a repeated-measures t-test to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 2.94. The treatment is expected to change scores on a task. Which of the following is the correct decision for a hypothesis test using α = .05.

Fail to reject the null hypothesis with either a one-tailed or a two-tailed test.

Reject the null hypothesis with a one-tailed test but fail to reject with two two-tailed test

Fail to reject the null hypothesis with a one-tailed test but reject with a two-tailed test.

Reject the null hypothesis with either a one-tailed or a two-tailed test.

Answer 1

researcher conducts a repeated-measures t-test to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 2.94

Thus test statistics value t = 2.94

We have n = 16

Given significance level α = .05

Criteria:- We reject null hypothesis , if calculated test statistics is greater t-critical value , where is t-distributed with n-1 degree of freedom at given significance.

Now we will find for one-tail test and for two tail test .

• For one tail test:- =

here is t-distributed with n-1= 16-1 = 15 degree of freedom at given significance α = .05 .

Thus =

If can be obtained from statistical book or from any software like R,excel etc.

From R

> qt(1-0.05,df=15)               #
[1] 1.75305

Hence = = 1.75305                   ( for one tail )

• For two tailed test:- =

here is t-distributed with n-1= 16-1 = 15 degree of freedom at given significance α = .05 .

Thus =

If can be obtained from statistical book or from any software like R,excel etc.

From R

> qt(1-0.05/2,df=15)           #
[1] 2.13145

Hence = = 2.13145           ( for two tailed test )

So we have t-critical value = = 1.75305 for one tailed test and = = 2.13145 for two tailed test .

Now we reject null hypothesis is test statistics value t is greater than respective t-critical values

1) For one tailed test

t = 2.94      ; = = 1.75305

Thus test statistics value t = 2.94 > 1.75305

Hence test statistics value t >

So we reject null hypothesis with one-tailed test

2) For two tailed test

t = 2.94      ; = = 2.13145

Thus test statistics value t = 2.94 > 2.13145

Hence test statistics value t >

So we reject null hypothesis with two-tailed test.

Hence we Reject the null hypothesis with a one-tailed test and also reject null hypothesis with two two-tailed test .

So correct option is

Option D) Reject the null hypothesis with either a one-tailed or a two-tailed test.