Question

Two researchers (A and B) compute a one-sample t test. For both tests, the mean difference...

Two researchers (A and B) compute a one-sample t test. For both tests, the mean difference between the sample and value stated in the null hypothesis is 5, but the standard error is smaller for Researcher A. Which test is more likely to result in a decision to reject the null hypothesis?

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Answer #1

Researcher A. test is more likely to result in a decision to reject the null hypothesis

Explanation:

Let

the standard error for Researcher A.= x

the standard error for Researcher B.= y

Given:

X < y

Also given:

= 5

So,

Test Statistic for Researcher A.is given by:

Test Statistic for Researcher B.is given by:

Since x< y, we note:

The hypothesis is rejected if t > tcrit

Since is greater of the 2 test statistics, we conclude that Researcher A. test is more likely to result in a decision to reject the null hypothesis

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