Plain M&M's come in 6 different colors (Blue, Orange, Green, Yellow, Red, Brown) and are produced...
Plain M&M's come in 6 different colors (Blue, Orange, Green, Yellow, Red, Brown) and are produced at two different plants. M&M's that come from a plant in Tennessee are supposed to have the following distribution of colors: 20.7% Blue; 20.5% Orange; 19.8% Green; 13.5% Yellow; 13.1% Red and 12.4% Brown. Quality control at the plant is concerned the machine is not working correctly and that it is producing a different distribution of colors. They take a random sample of 940 plain M&M's. A Chi-Square Goodness of Fit Test is performed. Calculate the value of the chi-square goodness of fit test statistic given the observed counts below. Enter your answer to 3 decimal places. You will need to enter the expected count for Blue from the previous problem; use the value to calculate the contribution to chi-square for the Blue category and total the last column to get the overall test statistic value.
| Color |
Observed Count |
Expected Count |
Contribution to the Chi-Square test statistic = (Observed - Expected)2/Expected |
| Blue | 185 | ||
| Orange | 195 | 192.70 | (195-192.7)2/192.70 = 0.027 |
| Green | 180 | 186.12 | (180-186.12)2/186.12 = 0.201 |
| Yellow | 140 | 126.90 | (140-126.90)2/126.90 = 1.352 |
| Red | 121 | 123.14 | (121-123.14)2/123.14 = 0.037 |
| Brown | 119 | 116.56 | (119-116.56)2/116.56 = 0.051 |
| Total | 940 |
Homework Answers
Value of chi square goodness of test statistic
= Total sum of contributions
= 0.027 + 0.201 + 1.352 + 0.037 + 0.051
= 1.668
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