Question

BACKGROUND: A researcher is conducting a study on features of learning technology and has chosen to examine the effects of three different learning methods on performance in a graduate course (i.e., Audio-supplement, visual-supplement, no supplement on final exam grade). A representative sample was selected and randomly assigned to each of the three study methods. The researcher hypothesized that those who received A/V supplemented materials would perform significantly better on the exam.

ANALYSIS: In comparing sample means, it turns out that the test statistic in this study is *F* (2, 149) = 1.7; the critical value for the test statistic is *F* = 2.1. What decision should the researcher make about the null hypothesis?

- A) Fail to reject the null hypothesis

- B) Reject the null hypothesis

- C) Not enough information to make this decision.

Explain how you came to this conclusion.

Step 1

Let µ_{1 }and µ_{2 }be the mean effect of Audio-supplement and visual supplement on final exam grade respectively.

The aim is to check whether those who received A/V supplemented materials would perform significantly better on the exam.

The null and the alternative hypothesis is,

H_{0}: µ_{1}= µ_{2}

H_{1}: The means are not equal.

Step 2

*Decision rule:*

- If the
*Fcal > F(k–1,N–k)*reject the null hypothesis. - Otherwise fail to reject the null hypothesis.

Here the critical value, *F*(2,149) = 1.9 and the *F*-statistics is 2.1.

*Conclusion:*

Here, the test statistic, 2.1 is greater than the critical value 1.9.

Therefore, by the decision rule, rej...

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