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
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. |
In a recently purchased pack of peanut M&M's, 9 of the 65 peanut M&M's were brown....
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