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 χ^{2}
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**

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