Quality control. Mars, Inc. says that the colors of its M&M's® candies are 14% yellow, 13% red, 20% orange, 24% blue, 16% green and 13% brown. (www.mms.com/ us/about/products/milkchocolate). On his way home from work the day he was writing these exercises, one of the authors bought a bag of plain M&M's. He got 29 yellow, 23 red, 12 orange, 14 blue, 8 green, and 20 brown. Is this sample consistent with the company's advertised pro- portions? Test an appropriate hypothesis and state your conclusion.

a) If the M&M's are packaged in the advertised proportions, how many of each color should the author have ex- pected in his bag of M&M's?

b) To see if his bag was unusual, should he test goodness- of-fit, homogeneity, or independence?

c) State the hypotheses.

d) Check the conditions.

e) How many degrees of freedom are there?

f) Find x2 and the P-value.

g) State a conclusion.