The number of grams of fiber per serving for a random sample of three different kinds of foods is listed. Is there sufficient evidence at the 0.05 level of significance to conclude that there is a difference in mean fiber content among breakfast cereals, fruits, and vegetables?


Breakfast cereals Fruits Vegetables

3 5.5 10
4 2 1.5
6 4.4 3.5
4 1.6 2.7
10 3.8 2.5
5 4.5 6.5
6 2.8 4
8 3
5


State the hypothesis and identify the claim (4 points):



Find the critical value (2 points):

k = d.f. N = k-1 =
N = d.f. D = N-k =
a= critical value =

This appears to be an ANOVA test.

H_{0}: \;\ {\mu}_{1}={\mu}_{2}={\mu}_{3}

H_{a}: \;\ \text{at least one mean is significantly different}

The F test statistic is 2.17

The F critical value is 3.47

Also, the p value is .14. Since it is greater than alpha=.05, we do not reject H0

Therefore, since the test stat < critical value, we DO NOT reject the null hypothesis.

There is not enough evidence at the .05 level to conclude that there is a difference in the means.

Try using one of the non parametric sign tests to find which ones. Or maybe the post hoc tests.