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wrote...
Posts: 221
3 weeks ago
Peanut M&Ms According to the Mars Candy Company, peanut M&M's are 12% brown, 15% yellow, 12% red, 23% blue, 23% orange, and 15% green. On a Saturday when you have run out of statistics homework, you decide to test this claim. You purchase a medium bag of peanut M&M's and find 39 browns, 44 yellows, 36 red, 78 blue, 73 orange, and 48 greens. Test an appropriate hypothesis and state your conclusion.
Textbook 

Stats: Modeling the World


Edition: 4th
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wrote...
Posts: 248
3 weeks ago
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We want to know if the distribution of colors in the bag matches the distribution stated by the Mars Candy Company.
H0: The distribution of colors in the bag matches the distribution stated by the Mars Candy Company.
HA: The distribution of colors in the bag does not match the distribution stated by the Mars Candy Company.
Conditions:
*Counted data: We have the counts of the number of peanut M&Ms of each color.
*Randomization: We will assume that each bag of peanut M&Ms represents a random
sample of peanut M&Ms.
*Expected cell frequency: There are a total of 318 peanut M&Ms. The smallest percentage of any particular color is 12% (brown and red), and we expect 318(0.12) = 38.16. Since the smallest expected count exceeds 5, all expected counts will exceed 5, so the condition is satisfied.
Under these conditions, the sampling distribution of the test statistic is χ2 with 6 - 1 = 5 degrees of freedom, and we will perform a chi-square goodness-of-fit test.

χ2 = = + +... = 0.7528
P-value = P(χ2 > 0.7528) = 0.980
A P-value this large says that if the distribution of colors in the bag matches the distribution stated by the Mars Candy Company, an observed chi-square value of 0.7528 would happen about 98% of the time. Thus, we fail to reject the null hypothesis. These data do not show evidence that the distribution of colors in the bag does not match the distribution stated by the Mars Candy Company.
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