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. The results for 400 M&M's sampled in a similar study are displayed in the table.

a. Assuming the manufacturer's stated percentages are accurate, calculate the expected numbers falling into the six categories.
b. Calculate the value of 2 for testing the manufacturer's claim.
c. Conduct a test to determine whether the true percentages of the colors produced differ from the manufacturer's stated percentages. Use α = .05.

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Brown Yellow Red Orange Green Blue Totl 40 50 40 100 75 85 50