(Solved): 4. Repeated-measures ANOVA Suppose you are interested in studying whether temperature affects spat ...

4. Repeated-measures ANOVA Suppose you are interested in studying whether temperature affects spatial reasoning abilities. You decide to test spatial reasoning using completion time scores for the paper-folding test with five people, repeating the test on each person with three different temperatures (40 degrees, 60 degrees, and 80 degrees Fahrenheit). In this experiment, the null hypothesis is that: O The completion time mean for at least one temperature is different from another O There are no individual differences in the completion time means O There are no differences in the mean completion times among the temperatures compared The factor of interest is the , and the dependent variable is the The results of the study are presented in the following data table. All scores are times necessary to complete the paper-folding task, recorded in seconds. Temperature Participant 40 Degrees 60 Degrees 80 Degrees Participant Totals A 3.41 3.40 3.49 P = 10.30 n 5 B 3.29 3.47 3.25 P = 10.01 k 3 ? 3.70 3.71 3.63 P = 11.04 N 15 D 3.68 4.08 P = 11.64 54.70 3.88 3.74 E 3.80 4.17 P = 11.71 ??? 200.4864 T = 17.88 T = 18.83 T = 17.99 SS=0.2335 SS = 0.1858 SS= 0.4866 = = = = The three treatments in the experiment define three populations of interest. You use an ANOVA to test the hypothesis that the three population means are equal. Present the results of your analysis in the following ANOVA table by entering the missing df values and selecting the correct values for the missing SS, MS, and F entries. (Note: For best results, retain at least two additional decimal points throughout your calculations. Depending on the order in which you do these calculations and the number of digits you retain, you may find slight rounding differences in the last digit between your answers and the answer choices.) ANOVA Table Source SS df MS F Between treatments Within treatments 0.0755 0.1973 Between subjects Error 14 9 Total F Distribution Numerator Degrees of Freedom = 26 Denominator Degrees of Freedom = 26 0 5000 1 1.00 5000 2 3 5 7 8 F Use the Distributions tool to find the critical value for a = 0.05. The critical value is F = At a significance level of a = 0.05, evaluate the null hypothesis that the population means for all treatments are equal. The null hypothesis is conclude that temperature affects spatial reasoning abilities. You