At an alpha level of 0.05, tes
At an alpha level of 0.05, test to determine if the means of thethree populations are equal. The data below is based on samplestaken from three populations. Sample 1 Sample 2 Sample 3 60 84 6078 78 57 72 93 69 66 81 66
Answer:
The data is :
| Sample 1 | Sample 2 | Sample 3 |
| 60 | 84 | 60 |
| 78 | 78 | 57 |
| 72 | 93 | 69 |
| 66 | 81 | 66 |
(1) Null andAlternative Hypotheses
The following null and alternative hypotheses need to betested:
Ho: μ1 = μ2 = μ3
Ha: Not all means are equal
The above hypotheses will be tested using an F-ratio for aOne-Way ANOVA.
(2) RejectionRegion
Based on the information provided, the significance level isα=0.05, and the degrees of freedom are df1=2 and df2=2,therefore, the rejection region for this F-test isR={F:F>Fc=4.256}
(3) TestStatistics
(4) Decision aboutthe null hypothesis
Since it is observed thatF=10.636>Fc=4.256, it is then concluded thatthe null hypothesis is rejected.
Using the P-value approach: The p-value is p=0.0043, and sincep=0.0043<0.05, it is concluded that the null hypothesis isrejected.
(5)Conclusion
It is concluded that the null hypothesis Ho isrejected. Therefore, there is enough evidence to claimthat not all 3 population means are equal, at the α=0.05significance level.
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