Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.

    1. State the null hypothesis and the alternate hypothesis.
    2. What is the decision rule?
    3. Compute SST, SSE, and SS total.
    4. Complete an ANOVA table.
    5. State your decision regarding the null hypothesis.
    6. 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.