A psychologist compares the mean amount of time of rapid-eye movement (REM) sleep for subjects under three conditions. She randomly assigns 12 subjects to the three groups, four per group. The sample means for the three groups were 18, 15, and 12. The table shows the ANOVA table from SPSS.
REM sleep

a. Report and interpret the P-value for the ANOVA F test.
b. For the Tukey 95% multiple comparison confidence intervals comparing each pair of means, the margin of error for each interval is 13.3. Is it true or false that since all the confidence intervals contain 0, it is plausible that all three population means equal 0.
c. Would the margin of error for each separate 95% confidence interval be less than 13.3, equal to 13.3, or larger than 13.3? Explain why.

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Source Group Error Total DF MS 2 72.00 36.00 0.79 .481 9 408.00 45.33 11 480.00