M&M/MARS, makers of M&M Chocolate Candies, conducted a national poll in which more than 10 million people indicated their preference for a new color. The tally of this poll resulted in the replacement of tan-colored M&Ms with a new blue color. In the brochure “Colors,” made available by M&M/MARS Consumer Affairs, the distribution of colors for the plain candies is as follows:
Brown: 30%
Yellow: 20%
Red: 20%
Orange: 10%
Green: 10%
Blue: 10%
In a follow-up study, samples of 1-pound bags were used to determine whether the reported percentages were indeed valid. The following results were obtained for one sample of 400 plain candies:
M&M Color Sample
Color
Observed Frequency
Brown
125
Yellow
100
Red
75
Orange
30
Green
40
Blue
30
Use α = 0.05 and determine whether these data conflict with the percentages reported by the company.
1. Calculate the numerical value of the test statistic. Round your answer to three decimal places.
2. How many degrees of freedom are there?
3. True or False: The data in the sample conflict with the percentages reported by the company in a statistically significant way.