Question

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.)

	Judge 1	Judge 2	Judge 3
Gymnast 1	7.9	8.7	7.6
Gymnast 2	6.5	7.8	8.6
Gymnast 3	7.8	7.7	7.8
Gymnast 4	9.4	9.4	8.3
Gymnast 5	6.4	6.6	7.0

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 "F" to 3 decimal places.)

	ANOVA Source of Variation SS df MS F p-value Rows Columns Error Total

a-2. If average scores differ by gymnast, use Tukey’s HSD method at the 5% significance level to determine which gymnasts’ performances differ. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.)

	Population Mean Difference Confidence Interval Does the mean score differ at the 5% significance level? μ1 − μ2 [ , ] μ1 − μ3 [ , ] μ1 − μ4 [ , ] μ1 − μ5 [ , ] μ2 − μ3 [ , ] μ2 − μ4 [ , ] μ2 − μ5 [ , ] μ3 − μ4 [ , ] μ3 − μ5 [ , ] μ4 − μ5 [ , ]

Answer 1

a-1)

ANOVA
Source of Variation	SS	df	MS	F	P-value
Rows	8.7000	4	2.1750	5.112	0.0242
Columns	0.4893	2	0.2447	0.575	0.5843
Error	3.4040	8	0.4255
Total	12.5933	14

a-2)

Tukey-Kramer Multiple Comparisons
	Sample	Sample			Absolute		Critical			confidence interval
Group	Mean	Size		Comparison	Difference		Range	Results		lower bound	upper bound
1: Gymnast 1	8.066667	3		Group 1 to Group 2	0.43		1.84	Means are not different		-1.41	2.27
2: Gymnast 2	7.633333	3		Group 1 to Group 3	0.30		1.84	Means are not different		-1.54	2.14
3: Gymnast 3	7.766667	3		Group 1 to Group 4	-0.97		1.84	Means are not different		-2.81	0.87
4: Gymnast 4	9.033333	3		Group 1 to Group 5	1.40		1.84	Means are not different		-0.44	3.24
5: Gymnast 5	6.666667	3		Group 2 to Group 3	-0.13		1.84	Means are not different		-1.97	1.71
				Group 2 to Group 4	-1.40		1.84	Means are not different		-3.24	0.44
Other Data				Group 2 to Group 5	0.97		1.84	Means are not different		-0.87	2.81
Level of significance	0.05			Group 3 to Group 4	-1.27		1.84	Means are not different		-3.11	0.57
Numerator d.f.	5			Group 3 to Group 5	1.10		1.84	Means are not different		-0.74	2.94
Denominator d.f.	8			Group 4 to Group 5	2.37		1.84	Means are different		0.53	4.21
MSW	0.4255
Q Statistic	4.8858

please revert for doubts/....