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 next table.

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 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.

Transcribed Image Text:

Brown Yellow Red Orange Green Blue 100 75 85 50 40 50 Total 400