According to the manufacturer of M&Ms, 12% of the peanut M&Ms in a bag should be brown, 15% yellow, 12% red, 23% blue, 23% orange, and 15% green. A student randomly selected a bag of peanut M&Ms. The student counted the number of M&Ms that were each color and obtained the results show in the table below. Test whether peanut M&Ms follow the distribution stated by M&Ms at 0.05 level of significance.

Color observed

brown 53

yellow 66

red 38

blue 96

orange 88

green 59

a.Stat H₀ and H₁.

b.Calculate expected values for all colors.

c.Calculate test statistic.

d.Find critical value for chi-square.

e.Find P-value

Make appropriate statistical and managerial decision