Question

In: Statistics and Probability

Mars Inc. claims that they produce M&Ms with the following distributions: Brown 30% Red 20% Yellow...

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 21 Yellow 21
Orange 15 Green 16 Blue 14


Using the ?2 goodness of fit test to determine if the proportion of M&Ms is what is claimed, what is the test statistic?

Solutions

Expert Solution

The distribution of colors in a bag of M&M as claimed by Mars Inc is

Color Probability
Brown           0.30
Orange           0.10
Red           0.20
Green           0.10
Yellow           0.20
Blue           0.10

The observed frequency of colors in a randomly selected bag of M&M is

Color Probability Observed Frequency (fo)
Brown           0.30 23
Orange           0.10 15
Red           0.20 21
Green           0.10 16
Yellow           0.20 21
Blue           0.10 14

We want to test the hypothesis that the distribution of colors claimed by Mars is a good description of the color found in a bag of M&M randomly selected from the grocery store shelf.

That is we want to test the following hypotheses

The total M&Ms in the bag is

If the claims of Mars inc were true (that is null hypothesis were true), then the number of Brown M&M in the bag should be 110*0.30 = 33

This is called expected frequency

The chi-square statistics is calculated as

the following tables shows the calculations

The values are

The value of test statistics is 7.67

The degrees of freedom is (number of groups -1) = (6-1) = 5

The chi-square critical value for alpha = 0.05 is obtained from the chi-square table for df=5 is 11.070

The test statistics of 7.67 is less than the critical value 11.070. That means we accept the null hypothesis.

We conclude that there is suffcient evidence to support the claim that the proportion of M&Ms is what is claimed by Mars Inc

orchestra answered 2 years ago
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