STATISTICS QUESTION - M&M Values chart
Question # 00025774
Posted By:
Updated on: 09/12/2014 01:15 AM Due on: 09/12/2014
M&M Values chart
One way that we could determine if the Mars Co. is true to its word is to sample a package of M&Ms and
do a type of statistical test known as a “goodness of fit” test. This type of statistical test allow us to
determine if any differences between our observed measurements (counts of colors from our M&M
sample) and our expected (what the Mars Co. claims) are simply due to chance or some other reason
(i.e. the Mars company’s sorters aren’t doing a very good job of putting the correct number of M&M’s in
each package). The goodness of fit test we will be using is called a Chi Square (X2) Analysis.
To test this hypothesis we will need to calculate the X2 statistic, which is calculated in the following way:
The chart below has the Observed M&M values in it. Fill in the rest of the chart where it is not shaded and
answer the questions that follow.
Data Chart 1
Brown
Observed (o)
Expected (e)
Blue
27
46
Color Categories
Orange
Green
Red
30
34
28
Yellow
Total
35
200
Difference (oe)
Difference Squared
(oe)2
(oe)2/e
? (d2/e) = X2
Note: Degrees of freedom = number of categories – 1
1.
What is the hypothesis scenario?
2. Based on our sample, should we accept or reject our null hypothesis? Why or why not?
One way that we could determine if the Mars Co. is true to its word is to sample a package of M&Ms and
do a type of statistical test known as a “goodness of fit” test. This type of statistical test allow us to
determine if any differences between our observed measurements (counts of colors from our M&M
sample) and our expected (what the Mars Co. claims) are simply due to chance or some other reason
(i.e. the Mars company’s sorters aren’t doing a very good job of putting the correct number of M&M’s in
each package). The goodness of fit test we will be using is called a Chi Square (X2) Analysis.
To test this hypothesis we will need to calculate the X2 statistic, which is calculated in the following way:
The chart below has the Observed M&M values in it. Fill in the rest of the chart where it is not shaded and
answer the questions that follow.
Data Chart 1
Brown
Observed (o)
Expected (e)
Blue
27
46
Color Categories
Orange
Green
Red
30
34
28
Yellow
Total
35
200
Difference (oe)
Difference Squared
(oe)2
(oe)2/e
? (d2/e) = X2
Note: Degrees of freedom = number of categories – 1
1.
What is the hypothesis scenario?
2. Based on our sample, should we accept or reject our null hypothesis? Why or why not?
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Solution: STATISTICS QUESTION - M&M Values chart Solution