With a two-tailed hypothesis test with a dependent samples t -test, if the stati

Question

With a two-tailed hypothesis test with a dependent samples t-test, if the statistic is -4.61 and the critical value is 2.571 at the .05 significance level, what conclusions can we draw?

We reject the null hypothesis; our sample means are not significantly different from one another.

We reject the null hypothesis; our sample means are significantly different from one another.

We fail to reject the null hypothesis; our sample means are not significantly different from one another.

We fail to reject the null hypothesis; our sample means are significantly different from one another.

We reject the null hypothesis; our sample means are not significantly different from one another.

We reject the null hypothesis; our sample means are significantly different from one another.

We fail to reject the null hypothesis; our sample means are not significantly different from one another.

We fail to reject the null hypothesis; our sample means are significantly different from one another.

Explanation / Answer

Given that,

With a two-tailed hypothesis test with a dependent samples t-test, if the statistic is -4.61 and the critical value is 2.571 at the .05 significance level,

Since it is two-tailed hypoyhesis test, there are two critical values that is -2.571 and +2.571

Decision rule based on critical values,

Reject null hypothesis (H0), if test statistic < -2.571 OR

test statistic > 2.571

Here, test statistic = -4.61 < Critical value = -2.571

Implies that, reject the null hypothesis.

Conclusion: There is a sufficient evidence to support the claim that the our sample means are significantly different from one another.

Hence,

Answer:

We reject the null hypothesis; our sample means are significantly different from one another.

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