Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.
- State the null hypothesis and the alternate hypothesis.
- What is the decision rule?
- Compute SST, SSE, and SS total.
- Complete an ANOVA table.
- State your decision regarding the null hypothesis.
- If H0 is rejected, can we conclude that treatment 1 and treatment 2 differ? Use the 95 percent level of confidence
Solution: We need to test the following hypotheses:
We use Excel again to perform an ANOVA analysis:
- The rejection rule is: We reject the null hypothesis if
- From the table we see that
- The F-statistics is equal to, which means that we reject the null hypothesis.
- We use a t-test to compare Treatment 1 and Treatment 2:
null hypothesis of equal means. This means that we have enough evidence to claim that Treatment 1 and Treatment 2 have different means.