Question

M&Ms are multicolored candies in a bag with six colors: Brown, Blue, Red, Yellow, Green and Orange. Mars now claims that all six colors are equally likely. In an attempt to reject the claim, an 8-oz bag of M&Ms was purchased and the colors counted. The results of the count are below. Does this sample contradict Mars’ claim when α = 0.10? Brown Blue Red Yellow Green Orange 37 41 32 25 36 39 If the claim is true what is the expected number of Blue M&Ms? How many degrees of freedom to you have for this chi-square problem? Find the test statistic χ² to two decimals.

Which of these is the correct range of p-values for this problem?

Select one:

0.25 < p < 0.50

0 < p < 0.005

0.005 < p < 0.010

0.05 < p < 0.10

Answer 1

Category	Observed Frequency (O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
Brown	37	1/6=0.1667	210 * 0.1667 = 35.007	(37 - 35.007)²/35.007 = 0.1135
Blue	41	0.1667	210 * 0.1667 = 35.007	(41 - 35.007)²/35.007 = 1.026
Red	32	0.1667	210 * 0.1667 = 35.007	(32 - 35.007)²/35.007 = 0.2583
Yellow	25	0.1667	210 * 0.1667 = 35.007	(25 - 35.007)²/35.007 = 2.8606
Green	36	0.1667	210 * 0.1667 = 35.007	(36 - 35.007)²/35.007 = 0.0282
Orange	39	0.1667	210 * 0.1667 = 35.007	(39 - 35.007)²/35.007 = 0.4555
Total	210	1.00	210.042	4.7419

Test statistic:  

χ² = ∑ ((O-E)²/E) = 4.74

df = n-1 = 5

p-value = CHISQ.DIST.RT(4.7419, 5) = 0.448

0.25 < p < 0.50