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(c)    Is the assumption of eąual standard deviations reasonable here? Explain why or why not.

(d)    Run the one-way ANOVA. Give the hypotheses tested, the test statistic with degrees of freedom, and the P-value. Summarize your conclusion.

12.17

Refer to the previous exercise. Use the Bonferroni or another multiple comparisons procedurę to compare the group means. Summarize the results and support your conclusions with a graph of the means.

12.18

Do piano lessons improve the spatial-temporal reasoning of preschool children? In Exercise 7.65 (page 546) we examined this ąuestion by comparing the change scores (after treatment minus before treatment) of 34 children who took piano lessons with the scores of 44 children who did not. The latter group actually contained three groups of children: 10 were given singing lessons, 20 had some Computer instruction, and 14 received no extra lessons. The data appear in Table 12.4.

(a)    Make a table giving the sample size, the mean, the standard deviation, and the standard error for each group.

(b)    Analyze the data using one-way analysis of variance. State the nuli and altemative hypotheses, the test statistic with degrees of freedom, the P-value, and your conclusion.