Question

The following are the weights of different brands of cereal. The results are listed below.

Brand A Brand B Brand C

32 27 22

34 24 25

37 33 32

33 30 22

36 21

1. At the 5% significance level, test the claim that the three brands have the same mean weight in ounces.

Answer 1

Null hypothesis ( H0 ) :  the three brands have the same mean weight in ounces.

Alternative hypothesis ( H1 ) :  the three brands have the different mean weight in ounces.

Anova table

For the given data using Anova single factor in Excel we get output as

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	221.7643	2	110.8821	7.011806	0.010883	3.982298
Within Groups	173.95	11	15.81364
Total	395.7143	13

test statistic = 7.01

So from the above output

Decision :

P value < l.o.s

0.01088 < 0.05

so reject Ho

Conclusion :

At alpha = 0.05 l.o.s there is no enough evidence to claim that the three brands have the same mean weight in ounces.