# Chi square Test- Goodness of Fit

Perform a Chi-Square Goodness of Fit (GOF) test to determine whether there is a difference between the observed values versus the expected values expected. The null hypothesis should be there is no statistical difference between the expected and observed distribution, and the alternate hypothesis is that there is a statistical difference between the distributions. This is a one-variable test. What you need to do first is calculate the expected values for each color from both the total number of M & M's and from the percentage expected for each color (M & M's actually published these percentages on its website). State all 5 of the steps, and use a .05 level of significance.

Color Number Expected

Observed Number

Brown 93 13%

Red 93 13%

Yellow 97 14%

Orange 149 20%

Blue 126 24%

Green 102 16%

660 100%

https://brainmass.com/statistics/chi-squared-test/chi-square-test-goodness-of-fit-199662

#### Solution Preview

Please see the attached file for complete solution. Formulas may not print here.

Solution:

Fo Fe Fe (Fo-Fe)^2 (Fo-Fe)^2/Fe

Brown 93 13% 85.8 51.84 0.6042

Red 93 13% 85.8 51.84 ...

#### Solution Summary

Solution describes the steps in calculating chi-square statistics from given expected and observed frquencies. Then, a chi-square test is carried out to check whether there is significant difference in observed and expected distribution.