Question

a. Given the following information obtained from four normally distributed populations, construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "SS" to 2 decimal places, "MS" to 4 decimal places, and "f' to 3 decimal places.) SST = 78.95; SSTR = 18. 16; C = 4; n1 = n2 = n3 = n4 = 15 df ANOVA Source of Variation Between Groups Within Groups Total p-value 0.002 b. At the 10% significance level, what is the conclusion to the ANOVA test of mean differences? Reject Ho; we can conclude that some means differ. Do not reject Ho; we cannot conclude that some means differ. Do not reject Ho; we can conclude that some means differ. Reject Ho; we cannot conclude that some means differ.

Answer 1

(a) c = 4, therefore df1 = c - 1 = 3

N = 15 * 4 = 60, therefore df2 = N - c = 60 - 4 = 56

SS within = SST - SSTR = 78.95 - 18.16 = 60.79

MSTR = SSTR / df1 = 18.16 / 3 = 6.0533

MS Within = SS within / df2 = 60.79 / 56 = 1.0855

F = MSTR / MS within = 6.0533 / 1.0855 = 5.577

The ANOVA table is below

Source	SS	DF	Mean Square	F	p - value
Between	18.16	3	6.0533	5.577	0.002
Within/Error	60.79	56	1.0855
Total	78.95	59

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(b) Since p value is < $\alpha$ (0.10), we reject H0

Option 1: reject H0. We can conclude that some means differ.