Ten observations were selected from each of three populations, and an analysis of variance was performed on the data. The following are the results:
Source ofVariationSum ofSquares
Degrees ofFreedom
MeanSquare
F
BetweenTreatments82.4
WithinTreatments(Error)158.4
?
a.Using ? = .05, test to see if there is a significant difference among the means of the three populations. State the null and alternative hypotheses.b.If, in Part a, you concluded that at least one mean is different from the others, determine which mean is different. The three sample means are 
= 24.8, 
= 23.4, and 
= 27.4.
Use ? = .05.
What will be an ideal response?
| a. | H0: ?1 = ?2 = ?3 Ha: at least one mean is different F = 7.02; p-value is less than .01; reject H0 |
| b. | LSD = 2.22 | - | = 1.4; | - | = 2.6; | - | = 4.0 |
The mean of the third population is different.
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