Question

Until very recently, company policy dictated that M&M bags include 30% brown, 20% yellow, 20% red, and 10% orange, blue, and green, respectively. After buying a bag of M&Ms, the author counted 29 yellow, 23 red, 12 orange, 14 blue, 8 green, and 18 brown. Is this sample consistent with the company’s stated proportions? Test an appropriate hypothesis and state your conclusion.

1. If the M&Ms are packaged in the stated proportions, how many of each color should the author have expected to get in his bag?
2. What is the appropriate test, and why?
3. State the hypotheses, check the conditions, and determine the degrees of freedom.

Find the chi-square statistic and p-value. State your conclusion.

Answer 1

Ans:

Chi square test for goodness of fit,as we want to check if sample data fits the stated distribution.

H0:The sample data fits the given distribution.

Ha:The sample data does not fit the given distribution.

degree of freedom=6-1=5

	Observed,fo	pi	Expected,fe	(fo-fe)^2/fe
Brown	18	0.3	31.2	5.585
yellow	29	0.2	20.8	3.233
red	23	0.2	20.8	0.233
orange	12	0.1	10.4	0.246
blue	14	0.1	10.4	1.246
green	8	0.1	10.4	0.554
Total	104	0.3	104	11.096

Test statistic:

Chi square=11.096

p-value=CHIDIST(11.096,5)=0.0495

Assume alpha=0.05

As,p-value<0.05,we reject H0.

There is sufficient evidence to conclude that sample is not consistent with the company’s stated proportions.