4. Hypothesis testing with ANOVA Aa Aa opinions about whether caffeine enhances

Question

4. Hypothesis testing with ANOVA Aa Aa opinions about whether caffeine enhances test performance differ. You design a study to test the impact of drinks with different caffeine contents on students' test-taking abilities. You choose 21 students at random from your introductory psychology course to participate in your study. You randomly assign each student to one of three drinks, each with a different caffeine concentration, such that there are seven students assigned to each drink. You then give each of them a plain capsule containing the precise quantity of caffeine that would be consumed in their designated drink and have them take an arithmetic test 15 minutes later. The students receive the following arithmetic test scores: Cola Black Tea Coffee Caffeine Content (mg/oz) 2.9 5.9 13.4 85 85 92 2X2 147,641 86 87 G 1,755 82 82 80 N m 21 75 75 89 k 3 66 88 96 78 76 83 87 82 559 T3 619 T2 577 SS1 338.86 SS 177.71 SS3 185.71 n2 M1 79.8571 M2 82.4286 M3 m 88.4286 You plan to use an ANovA to test the impact of drinks with different caffeine contents on students' test-taking abilities. What is the null hypothesis?

Explanation / Answer

The null hypothesis

The populationmean test scores for all three treatments are equal

Filled in ANVOA

Source

SS

Df

MS

Between

973.14-702.28=270.86

3-1=2

270.86/2=135.43

Within

702.28

21-3=18

702.28/18=39.02

Total

973.14

3*7-1=20

F-ratio=Between Mean Sqaure/Within Mean Sqaure=135.43/39.02=3.47

F=135.43/39.02=3.47

Thus, F=3.47

Choose middle radio button for graph, 2 as numerator df and 18 as denominator df so that F=3.55

Conclusion: Option-III

Source

SS

Df

MS

Between

973.14-702.28=270.86

3-1=2

270.86/2=135.43

Within

702.28

21-3=18

702.28/18=39.02

Total

973.14

3*7-1=20

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