Test the claim that the samples come from populations with the same mean. Assume that the...
Test the claim that the samples come from populations
with the same mean. Assume that the populations are normally
distributed with the same variance.
Given the sample data below, test the claim that the populations
have the same mean. Use a significance level of 0.05.
a. test statistic
b. critical value
Homework Answers
applying ANOVA:
| Group | ni | x̅i | S2i | ni*(Xi-Xgrand)2 | (ni-1)*S2i |
| A | 10 | 32.9 | 3.1600 | 56.011 | 28.4400 |
| B | 10 | 31.6 | 3.0400 | 11.378 | 27.3600 |
| C | 10 | 27.1 | 4.6600 | 117.878 | 41.9400 |
| grand mean= | 30.5333 | 185.2667 | 97.7400 | ||
| SSTr | SSE | ||||
| Source | SS | df | MS | F | Fcrit |
| between | 185.2667 | 2 | 92.6333 | 25.589 | 3.3541 |
| within | 97.7400 | 27 | 3.6200 | ||
| total | 283.0067 | 29 |
a)
test statistic F =25.589
b)
critical value at (2.27) degree of freedom and 0.05 level =3.354
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