The table below contains three samples obtained from three different populations

Question

The table below contains three samples obtained from three different populations. Please conduct an ANOVA test for the equality of the three population means and state if the test rejects the null hypothesis of the equality of the three means at the 90% confidence level?

Sample 1

Question 1 options:

The test fails to reject the null hypothesis that the three means are equal.

The test rejects the null hypothesis that the three means are equal

The test is inconclusive

Sample 1

Sample 2 Sample 3 7 11 6 5 8 5 7 11 4 6 7 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

Explanation / Answer

Below is the output from Minitab

One-way ANOVA: Sample 1, Sample 2, Sample 3

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level = 0.05
Rows unused 2

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 Seq SS Contribution Adj SS Adj MS F-Value P-Value
Factor 2 28.93 8.45% 28.93 14.463 2.26 0.115
Error 49 313.31 91.55% 313.31 6.394
Total 51 342.23 100.00%

Model Summary

S R-sq R-sq(adj) PRESS R-sq(pred)
2.52863 8.45% 4.72% 354.712 0.00%

Means

Factor N Mean StDev 95% CI
Sample 1 18 7.444 1.247 (6.247, 8.642)
Sample 2 18 9.222 2.157 (8.025, 10.420)
Sample 3 16 8.125 3.722 (6.855, 9.395)

Pooled StDev = 2.52863

   F Cal = MS Between / Ms Within = 2.26                                       
MAKE DECISION                          
   Hence Value of 0.115 > 0.05 and Here We Failed Reject Ho                      

[ANSWER]

The test fails to reject the null hypothesis that the three means are equal.

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