Question

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? as of 1/9/13 (latest reported data) M&M'S CHOCOLATE CANDIES mix is: M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown. M&M'S PEANUT: 23% cyan blue, 23% orange, 15% green, 15% bright yellow, 12% red, 12% brown. M&M'S KIDS MINIS: 25% cyan blue, 25% orange, 12% green, 13% bright yellow, 12% red, 13% brown. M&M'S DARK: 17% cyan blue, 16% orange, 16% green, 17% bright yellow, 17% red, 17% brown. M&M'S PEANUT BUTTER and ALMOND: 20% cyan blue, 20% orange, 20% green, 20% bright yellow, 10% red, 10% brown. M&M'S PRETZEL: 28.5% blue, 14.3% each of yellow, orange, green, brown and red. M&M'S COCONUT: 37.5% white, 37.5% brown and 25% green .. discuss this information above

Answer 1

A sample bag of 65 peanut M&Ms contained the following colors ...
Cyan blue	13
Orange	15
Green	8
Bright yellow	7
Red	13
Brown	9

	Expected %	Sample %	95% confidence interval
Cyan blue	23%	20.00%	[10.28%, 29.72%]
Orange	23%	23.08%	[12.84%, 33.32%]
Green	15%	12.31%	[4.32%, 20.30%]
Bright yellow	15%	10.77%	[3.23%, 18.31%]
Red	12%	20.00%	[10.28%, 29.72%]
Brown	12%	13.85%	[5.45%, 22.25%]

95% confidence intervals:
Cyan blue				Bright yellow
Confidence interval - proportion				Confidence interval - proportion
	95%	confidence level			95%	confidence level
	0.2	proportion			0.1077	proportion
	65	n			65	n
	1.960	z			1.960	z
	0.097	half-width			0.075	half-width
	0.2972	upper confidence limit			0.1831	upper confidence limit
	0.1028	lower confidence limit			0.0323	lower confidence limit
Orange				Red
Confidence interval - proportion				Confidence interval - proportion
	95%	confidence level			95%	confidence level
	0.2308	proportion			0.2	proportion
	65	n			65	n
	1.960	z			1.960	z
	0.102	half-width			0.097	half-width
	0.3332	upper confidence limit			0.2972	upper confidence limit
	0.1284	lower confidence limit			0.1028	lower confidence limit
Green				Brown
Confidence interval - proportion				Confidence interval - proportion
	95%	confidence level			95%	confidence level
	0.1231	proportion			0.1385	proportion
	65	n			65	n
	1.960	z			1.960	z
	0.080	half-width			0.084	half-width
	0.2030	upper confidence limit			0.2225	upper confidence limit
	0.0432	lower confidence limit			0.0545	lower confidence limit

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 peanut M&Ms has colors as claimed.