Question

Item	Group 1	Group 2	Group 3
1	14	17	17
2	13	16	14
3	12	16	15
4	15	18	16
5	16		14
6			16

a. Conduct a one-way analysis of variance on the data assuming the populations have equal variances and the populations are normally distributed. Use alpha = 0.05.

b. If warranted, use the Tukey-Kramer procedure to determine which populations have different means. Use an alpha level of 0.05.

Answer 1

Groups	Count	Sum	Average	Variance
Group 1	5	70	14	2.5
Group 2	4	67	16.75	0.916667
Group 3	6	92	15.33333	1.466667

a) One Way ANOVA:

and (Atleast one is not equal)

Significant value= 0.05

The test statistic:

Grand mean:

P-value: 0.025853

The test statistic is significant and rejects H0. There is sufficient evidence to support the claim that there is statistical difference between sample means.

b) Tukey's mean difference:

To be non significant:

Mean difference between 1 and 2: |14-16.75|= 2.75

|M1-M2| > T is significant.

Mean difference between 1 and 3: |M1-M3|= 1.333

|M1-M2| < T is not significant.

Mena difference between 2 and 3: |M2-M3|= 1.41667

|M2-M3| < T is not significant.

Group1 and 2 are significantly different.