## Wednesday, January 21, 2015

### M&M Hypothesis Test

This activity will make use of the data you gathered in M&M Activity.

As has been observed, there are six colors typically found in each bag of M&Ms. In the previous blog post, we tested whether the proportions of color within each bag remained consistent with differences due to no more than random variation.

Using data I had gather, I hypothesize that each bag of M&Ms contains 18 total and that each of the colors has the following average:
Red 3
Orange 3
Yellow 2.5
Green 4
Blue 4
Brown 1.5

In order to perform this test, we use a table of the following type.

There are blanks to be filled in depending the particular putative mean and the set level of significance.  I chose to test the green at a 0.05 level of significance.(The level of significance is chosen ahead of time so as not to effect the decision.)  This gave me the following table:

This is a small sample of size n=10 with 9 degrees of freedom, so I used the T-table* to give me a critical number of 2.262.  The number of greens from my sample was: 5,5,4, 3,3,3,3,4,3,1.  This has an average of 3.4 and a standard deviation of 1.2,  The calculation and test were completed as follows:
In this case, I could not prove that the average is not 4.

Follow these procedures yourself and test at a 0.10 level of significance. You will have to look up a new T-value, but as you sample size is n=10, it will still have 9 degrees of freedom. Also test whether the number of M&Ms per bag is 18.

*(In order to use the T-statistic, we have to assume that the data is normally distributed. This can be justified, but it is beyond the scope of the current activity.)