Question

Mars Inc. claims that they produce M&Ms with the following distributions:

Brown	30%	Red	20%	Yellow	20%
Orange	10%	Green	10%	Blue	10%

A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were:

Brown	23	Red	23	Yellow	20
Orange	15	Green	17	Blue	15

Using the χ² goodness of fit test to determine if the proportion of M&Ms is what is claimed, what is the test statistic?

a) χ² = 10.409

b) χ² = 1.960

c) χ² = 9.109

d) χ² = 7.209

e) χ² = 18.218

f) None of the above

Answer 1

Here we have to test the hypothesis that,

H0 : All the population proportions are equal.

H1 : Atlease one population proportion differ.

Assume alpahaa = 0.05

The test statistic follows X² distribution with k-1 degrees of freedoms.

where k = no. of groups= 6

The test statistic is,

where O is observed frequency

E is expected frequency.

We have given proportions and O.

Now we can find E by using formula,

E = N*p

where N = 113

colour	p	E	O	(O-E)^2/E
brown	0.3	33.9	23	3.50472
red	0.2	22.6	23	0.00708
yellow	0.2	22.6	20	0.299115
orange	0.1	11.3	15	1.211504
green	0.1	11.3	17	2.875221
blue	0.1	11.3	15	1.211504
total		113	113	9.109145

Test statistic = 9.109

Option c) is correct.