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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. What is the expected count for Blue M&M's based on this sample of n=940 plain M&M's? Enter your answer to two decimal places.

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
Math   Statistics-And-Probability   
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