Question

The M&Ms milk chocolate color distribution is the following: 25% blue, 35% orange, 23% red, and 17% brown. In a bag, I found 164 blue M&Ms, 239 orange ones, 170 red ones and 136 brown ones. I am wondering whether my bag of M&Ms is representative of the manufacturer’s claim. Calculate the absolute value of the test statistic.

Answer 1

1646.857

Explanation:

The test statistic is obtained using the relation :

χ² = Σ (observed - Expected)² / expected

The observed values :

Blue = 164 ; Orange = 239 ; Red = 170 ; Brown = 136

Expected values:

Blue = 0.25 * 164 = 41 ;

Orange = 0.35 * 239 = 83.65

Red = 0.23 * 170 = 39.1

Brown = 0.17 * 136 = 23.12

Blue = (164-41)^2 / 41 = 369

Orange = (239 - 83.65)^2 / 83.65 = 288.507

Red = (170 - 39.1)^2 / 39.1 = 438.230

Brown = (136 - 23.12)^2 / 23.12 = 551.12

χ² = (369 + 288.507 + 438.230 + 551.12)

χ² = 1646.857