GOODNESS OF FIT WORKSHEET

The following is a quote from the Mars Company, maker of M&M candies:

We can assure you that the colors are blended mechanically according to the formula.Our present means of color dispensing should place a fairly uniform blend of colors in every package;however, occasionally an unusual assortment of colors may appear.

The theoretical percentages of each color (as given by the M&M company) are:

Red

Yellow

Green

Orange

Blue

Brown

Plain

13%

14%

16%

20%

24%

13%

Peanut

12%

15%

15%

23%

23%

12%

1. Each student will need to buy a package of regular colors, Milk Chocolate M&M's (plain or peanut) that is at least 4 oz. (colors of red, yellow, green orange, blue, brown) to be used for this project. All students will complete this test for your individual bag of M&Ms to receive credit You will then report your test results (reject or fail to reject Ho) and numbers to your group leader.

Red

Yellow

Green

Orange

Blue

Brown

Total

Yours

Group

Expected value

1. The group leader will total the group values and will sum the colors. After working as a group to complete this test using the group totals, the leader will post the group results and the decision results of each individual in the group (reject or fail to reject Ho).Only the names of individuals that submit their test results to the group leader will be included on the group posting for credit.

You will conduct a goodness of fit test to determine whether your and the group frequency numbers for each color "fit" the expected values.Remember to complete your individual test first then send your results and numbers to the group leader.Be sure and work with the group leader to complete the group test.Use a significance level of 0.05.

1. Determine the expected values for all colors of the M&Ms.Use the number of M&Ms from the whole group (when doing the group test).Be sure you use the correct type of M&M given percentages (plain or peanut).

2. Write the null and alternate hypotheses.Remember these two statements must include all possible outcomes.

Ho:

H₁:

3. Find the Chi-square critical value.

4. Compute the test statistic value.

5. What is the statistical decision about null hypothesis?

6. Write a conclusion about the Mars Company's claim regarding the colors of the M&Ms by interpreting your decision in Question 6.