## Question 855:

1

1. Q855_1_ANOVA_tableQ855.xls
We need to know the break-down of the ANOVA table to complete this one.

a. Since we are using the ANOVA to compare multiple means, the Null Hypothesis is that all means are equal. The Alternative Hypothesis is that at least one mean is different than the others.
b. We wll reject the Null Hypothesis if we obtain an F-ratio with a p-value below .05. We need to obtain a F-statistic using 2 and 12 degrees of freedom for a .05 alpha. The 2 df come from 3-1 and 12 comes from the total degrees of freedom (14) minus the treatment degrees of freedom. We can use the excel function =FINV(0.05,2,12) = 2.61. So we need to obtain an F-statistic above 2.61 to reject the Null.
c. I've attached the ANOVA table in an excel file which shows how the Sum of Squares leads to the test statistic F. We obtain the F-ratio of 9, which is well above 2.61.
d. Since the p-value is less than .05 we reject the Null Hypothesis. We conclude that there is a difference between the means.