Question

5. Hypothesis testing with ANOVA Aa Aa E 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: Water Cola 2.9 Coffee 13.4 Caffeine Content (mg/oz) 92 87 EX2 = 141,479 G = 1,715 N = 21 k = 3 89 96 92 T1 = 537 T2 = 559 T3 = 619 SS1 = 381.43 SS2 = 338.86 SS3 = 185.71 ni = 7 n2 = 7 n3 = 7 M2 = 76.7143 M2 = 79.8571 M3 = 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? O O O The population mean test scores for all three treatments are not all equal. The population mean test scores for all three treatments are different. The population mean test score for the water population is different from the population mean test score for the cola population The population mean test scores for all three treatments are equal. O

Answer 1

• The population mean test scores of all three treatements are equal Source ss 1420.67-906 of Between Ms 514.67 = 257.335 z 514.671 within 906 21-3 1906 150.333] 18+2=2011 Total 14 20.67

Mean Gaane sum of square b/w the groups | I The error Meam Sum of square F MSB 257.335 MSB] MSE 257.335 *150.333 MSE 50.333 D F = 5.113] P-value = P(F>50113 ) =FDIST (2.113,2, 28) - 0.0174 P-value is less them 0.05; so, Reject Ho You can reject the null hypothesis; caffine dies appear to offect test-performance
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