M&M's plain chocolate candies come in six different colors: dark brown, yellow, red, orange, green, and blue.

According to the manufacturer (Mars, Inc.), the color ratio in each large production batch is 30% brown, 20%

yellow, 20% red, 10% orange, 10% green, and 10%

blue. To test this claim, a professor at Carleton College

(Minnesota) had students count the colors of M&M's found in "fun size" bags of the candy (Teaching Statistics, Spring 1993). The results for 370 M&M's are displayed in the table below.

Brown Yellow Red Orange Green Blue Total

a. Assuming the manufacturer's stated percentages are accurate, calculate the expected numbers falling into the six categories.

b. Calculate the value of X2 for testing the rnanufacturer's claim.

c. Conduct a test to determine whether the true percentages of the colors produced differ from the manufacturer's stated percentages. Use a = .05.