Question

State the null and alternative hypotheses. It has been rumored that the color distribution of M&M’s is 30% brown, 20% yellow, 20% red, 10% orange, 10% blue, and 10% green. You suspect this rumor is incorrect and decide to count how many of each color are contained in a randomly chosen bag in order to perform a Chi-Square goodness-of-fit test at a 5% significance level.

Color Brown Yellow Red Orange Blue Green Total

Observed 27 16 21 12 9 15 100

State the null and alternative hypotheses.

a) 0 : .3, .2, .2, .1, .1, .1 : At least one of the stated proportions is not correct brown yellow red orange blue green A H p p p p p p H      

b) 0 : .3, .2, .2, .1, .1, .1 : All of the stated proportions are not correct brown yellow red orange blue gree

Answer 1

The null hypothesis of chi square test is whether the proportions are same as defined

Null hypothesis:

The proportion of colors are as follows.

Brown	yellow	red	Orange	blue	green
0.3	0.2	0.2	0.1	0.1	0.1

Alternate hypothesis:

At least one of the stated proportions is not correct

Brown	yellow	red	Orange	blue	green
0.3	0.2	0.2	0.1	0.1	0.1