Question

In a package of any type of M&M, the M&M Mars company claims there is a certain percentage of each color. For example, in a package of peanut M&M's in the USA; 12% are brown, 12% are red, 15% are yellow, 23% are blue, 15% are green and 23% are orange. In a recently purchased pack of peanut M&M's, 9 of the 65 peanut M&M's were brown. If we were to use this sample to create a 95% confidence interval, we would get an interval (0.055 < p < 0.222). The Task - buy a package of M&Ms, the package must be larger than a fun-size (+50 pieces) - determine the claimed population percentage of each color M&M (see below) - record the total number of each color M&M in your package - determine the percentage of each color M&M in your package - create a confidence interval for each color M&M in your package - explain any discrepancies between the expected value and the values observed. Did you get the colors you expected? Any results you did not expect? Were the results closer than you expected?

Answer 1

A sample bag of 75 M&Ms contained the following colors ...
Brown	11
Red	12
Yellow	10
Blue	19
Green	10
Orange	13

95% confidence intervals:
Brown and Red
Confidence interval - proportion
	95%	confidence level
	0.12	proportion
	75	n
	1.960	z
	0.074	half-width
	0.1935	upper confidence limit
	0.0465	lower confidence limit
Yellow and Green:
Confidence interval - proportion
	95%	confidence level
	0.15	proportion
	75	n
	1.960	z
	0.081	half-width
	0.2308	upper confidence limit
	0.0692	lower confidence limit
Blue and Orange:
Confidence interval - proportion
	95%	confidence level
	0.23	proportion
	75	n
	1.960	z
	0.095	half-width
	0.3252	upper confidence limit
	0.1348	lower confidence limit

	Expected %	Sample %	95% confidence interval
Brown	12%	14.67%	[4.65%, 19.35%]
Red	12%	16.00%	[4.65%, 19.35%]
Yellow	15%	13.33%	[6.92%, 23.08%]
Blue	23%	25.33%	[13.48%, 32.52%]
Green	15%	13.33%	[6.92%, 23.08%]
Orange	23%	17.33%	[13.48%, 32.52%]
We see from the 95% confidence interval column that we have got all colors as expected.
None of the results are close.
This bag of M&Ms has colors as claimed.