Question

HWCh13 ANOVA Saved 4 Exercise 13-67 Algo 59 points At a gymnastics meet, three judges evaluate the balance beam performances of five gymnasts. The judges use a scale of 1 to 10, where 10 is a perfect score. A statistician wants to examine the objectivity and consistency of the judges. Assume scores are normally distributed. (You may find it useful to reference the q table.) eBook Gymnast 1 Gymnast 2 Gymnast 3 Gymnast 4 Gymnast 5 Judge 1 9.4 9.3 8.4 9.2. 9.8 Judge 2 7.7 7.8 6.1 8.1 9.3 Judge 3 9.1 7.1 6.4 7.5 9.0 Print Click here for the Excel Data File References a-1. Construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "SS", "MS", "p-value" to 4 decimal places and "P' to 3 decimal places.) SS df F 7.621 ANOVA Source of Variation Rows Columns Error Total 41 2 MS 2.3677 3.3140 0.3107 p-value 0.0078 0.0055 9.4707 6.6280 2.4853 18.5840 10.667 8 14 a-2. At the 5% significance level, can you conclude that average scores differ by judge? No, since the p-value for judge is greater than significance level. O No, since the p-value for judge is less than significance level. Yes. since the p-value for judge is greater than significance level. Yes, since the p-value for judge is less than significance level.

Answer 1

a-1)

Source of Variation	SS	df	MS	F	P-value
Rows	9.4707	4.0000	2.3677	7.621	0.0078
Columns	6.6280	2.0000	3.3140	10.667	0.0055
Error	2.4853	8.0000	0.3107
Total	18.5840	14.0000

a-2)

Yes since the p-value for judge is less than significance level.

b)

Yes. since the p-value for gymnast is less than significance level.

c)

MSE=			0.31
df(error)=			8
number of treatments =			5
pooled standard deviation=Sp =√MSE=			0.557

critical q with 0.05 level and k=5, N-k=8 df=			4.89
Tukey's (HSD)=w =(q/√2)*(sp*√(1/ni+1/nj) =			1.57

			Lower bound	Upper bound	differ
	(xi-xj )	ME	(xi-xj)-ME	(xi-xj)+ME
μ1-μ2	0.67	1.57	-0.91	2.24	not significant difference
μ1-μ3	1.77	1.57	0.19	3.34	significant difference
μ1-μ4	0.47	1.57	-1.11	2.04	not significant difference
μ1-μ5	-0.63	1.57	-2.21	0.94	not significant difference
μ2-μ3	1.10	1.57	-0.47	2.67	not significant difference
μ2-μ4	-0.20	1.57	-1.77	1.37	not significant difference
μ2-μ5	-1.30	1.57	-2.87	0.27	not significant difference
μ3-μ4	-1.30	1.57	-2.87	0.27	not significant difference
μ3-μ5	-2.40	1.57	-3.97	-0.83	significant difference
μ4-μ5	-1.10	1.57	-2.67	0.47	not significant difference