In a study of balloon angioplasty, patients with coronary artery disease were randomly assigned to one of four treatment groups: placebo, probucol (an experimental drug), multivitamins (a combination of beta carotene, vitamin E, and vitamin C), or probucol combined with multivitamins. Balloon angioplasty was performed on each of the patients. Later, "minimal luminal diameter" (a measurement of how well the angioplasty did in dilating the artery) was recorded for each of the patients. Summary statistics are given in the following table.40

(a) Complete the ANOVA table and bracket the P-value for the F test.

(b) What is the value of the F test statistic for testing that the effects of the four treatments are equal?
(c) How many degrees of freedom are there for the test from part (b)?
(d) The P-value for a one-way ANOVA F test is 0.0006. If α = 0.01, what is your conclusion regarding the null hypothesis?

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Probucol Multi and multi- Placebo Probucol vitamins vitamins 1 62 58 54 56 Mean 143 9 40 SD 1.79 0.45 154 0.61 0.58 0.55 a SS MSF df Source Between treatments Within treatments Total 5.4336 229 73.9945