Test the claim that the samples come from populationswith the same mean. Assume

Question

Test the claim that the samples come from populationswith the same mean. Assume that the populations are normallydistributed with the same variance.
At the 0.025 significance level, test the claim that the threebrands have the same mean if the following sample results have beenobtained
Brand A Brand B Brand C 32 27    22 34 24    25 37 33    32 33 30    22 36    21 39
Test the claim that the samples come from populationswith the same mean. Assume that the populations are normallydistributed with the same variance.
At the 0.025 significance level, test the claim that the threebrands have the same mean if the following sample results have beenobtained
Brand A Brand B Brand C 32 27    22 34 24    25 37 33    32 33 30    22 36    21 39

Explanation / Answer

ONE WAYANOVA - Assumptions

— Samples independency

— Normality

— Homogeneity of Variance

HYPOTHESES TO BE TESTED

Step 1:

Nullhypothesis:

H0: 1=2=3

That is, thereis no difference in the mean among different level of thebrands.

Alternative hypothesis:

H1:1 2 3

That is, thereis a difference in the mean among different level of thebrands

Step2

Levelof Significance: =0.025

Step3

We obtain thecalculated value by carrying out the following procedures inMEGASTAT

Output is shownbelow:

The F calculatedvalue is 12.12

Step4

Decision Rule: Reject the nullhypothesis if p-value < 0.025

Step5

Result: Since the p-value is less than0.05, the null hypothesis is rejected and we conclude that there isa difference in the mean among different level of thebrands

One factor ANOVA



Mean n Std. Dev 35.2 6 2.64 A 28.5 4 3.87 B 24.4 5 4.51 C 29.8 15 5.89 Total


ANOVAtable


Source SS    df MS F    p-value Treatment 325.37 2 162.683 12.12 .0013 Error 161.03 12 13.419
Total 486.40 14

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