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: Plain Peanut Red 13% 12% Yellow 14% 15% Green 16% 15% Orange 20% 23% Blue Brown 24% 13% 23% 12% A. Each person will need to buy a package of regular colors, Milk Chocolate M&M's that is at least 4 oz. (colors of red, yellow, green orange, blue, brown) to be used for this project. Exchange your counts with the members of your group to get the total for the group. We used two 8 OZ bags of regular M&Ms. Red Yours 39 Partner 37 Group 76 Expected 67.21 value Yellow 42 45 87 72.38 Green 52 50 102 82.72 Orange 43 45 88 103.4 Blue 45 42 87 124.0 8 Brown 38 39 77 67.21 Total 259 258 517 517 B. Group Leader will total the group values and will sum their color. After consulting with the rest of the group on the answers to these questions, the leader will need to post the totals and the answers on the bulletin board. You will conduct a goodness of fit test to determine whether the group frequency numbers for each color \"fit\" the expected values. Use a significance level of 0.05. 1. Determine the expected values for all of the M&Ms. Use the number of M&Ms from the whole group. Filled in on Chart 2. Write the null and alternative hypotheses. Remember these two statements must include all of the possible outcomes. 1 310316 Ho: H1 : 3. Compute the Chi-square critical value. 4. Compute the test statistic value. 5. Write a statistical decision about null hypothesis. 6. Write a conclusion about the colors of the M&Ms by interpreting your decision in Q5. 2 310316