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Consider the data in the table collected from four independent populations.
| Sample 1 | Sample 2 | Sample 3 | Sample 4 |
|---|---|---|---|
| 2 | 19 | 14 | 11 |
| 4 | 14 | 15 | 8 |
| 5 | 15 | 23 | 5 |
| 9 | 10 |
a) Calculate the total sum of squares (SST).
b) Partition the SST into its two components, the sum of squares between (SSB) and the sum of squares within (SSW).
c) Using a = 0.05, what conclusions can be made concerning the population means?
d) Test the hypothesis by first stating the null and the alternative hypotheses.
Let u1. u2, u3, and u4 be the population means of samples 1, 2, 3, and 4, respectively. What are the correct hypotheses for a one-way ANOVA test?