Question

The table below presents three samples of data.

Which of the following confidence levels would reject the null hypothesis that the three population means are equal?

Sample 1	Sample 2	Sample 3
7	11	6
5	8	5
7	11	4
6	7	5
6	13	14
6	13	5
6	12	5
6	11	6
8	8	8
9	7	6
7	6	14
9	7	4
8	8	8
8	9	13
9	6	10
8	11	14
8	9	14
9	12	8
6	11
8	12
12	9
11	5

Question 2 options:

	85%
	95%
	99%
	None of the above

Answer 1

Sample 1	Sample 2	Sample 3
7	11	6
5	8	5
7	11	4
6	7	5
6	13	14
6	13	5
6	12	5
6	11	6
8	8	8
9	7	6
7	6	14
9	7	4
8	8	8
8	9	13
9	6	10
8	11	14
8	9	14
9	12	8
6	11
8	12
12	9
11	5

One-way ANOVA

Method

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
Factor	3	Sample 1, Sample 2, Sample 3

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	2	31.88	15.940	2.14	0.127
Error	59	439.47	7.449
Total	61	471.35

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
2.72924	6.76%	3.60%	0.00%

Means

Factor	N	Mean	StDev	95% CI
Sample 1	22	7.682	1.729	(6.517, 8.846)
Sample 2	22	9.364	2.441	(8.199, 10.528)
Sample 3	18	8.278	3.847	(6.991, 9.565)

Pooled StDev = 2.72924

Here the p-value is 0.127. so we can reject the null hypothesis if level of significance is greater than 12.7%.

At 85% confidence level, level of significance is 15% which is greater than 12.7%.

Hence at 85% confidence levels we can reject the null hypothesis that three population means are equal.