Question

# 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 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

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,

$X^2 = \sum \frac{(O-E)^2}{E}$

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.

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