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:
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:
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.)