Question

ONE WAY ANOVA

Assume that you are a nutritionist who has been asked to determine whether there is a difference in sugar content among the three leading brands of breakfast cereal – Kelloggs, Post, and General Mills. To assess the amount of sugar in the cereals, you randomly sample six types of cereal for each brand and chemically determine the sugar content. The following grams of sugar were found:

Group 1           Group 2           Group 3
Kellogg’s           Post               General Mills

1               7               6
2               5               4
3               3               4
3               7               5
2               4               7
6               7               8

Please state your null hypothesis and alternative hypothesis, both as an equation and in your own words. After you run the data through SPSS, please write up the results.

Answer 1

Solution

We will use SPSS to solve to problem

Define the null and alternative hypothesis

H0: µ₁= µ₂= µ₃

H1 : At least one of the µ_i different from other

In words

H0 :  There is no difference in sugar content among the three leading brands of breakfast cereal – Kelloggs, Post, and General Mills.

H1 : At least one of the leading brands is different from other two brands.

Decision : Since the P-value = 0.019 < 0.05 so we reject the null hypothesis.

Conclusion : We have enough evidence to claim that there is a difference in sugar content among the three leading brands of breakfast cereal – Kelloggs, Post, and General Mills, at 0.05 level of significance.