Making Statistics Sweet on Valentine's Day
Planning on giving a bag of M&M's to your sweetie this Valentine's Day? Well, you can woo your Valentine with not only the gift of candy, but also the statistics behind those candy-coated chocolate pieces.
Are there equal amounts of each color in a bag?
You can record your counts of each color in the bag in a Minitab worksheet, and then use a pie chart (Graph > Pie Chart) to visualize the counts:
There were 138 blue M&M’s and only 63 red M&M’s in our sample. But is the difference between these counts statistically significant? A Chi-square test can tell us:
The p-value of 0.000 suggests that the observed counts are significantly different than what we would expect to see if there were an equal number of red, orange, yellow, green, blue and brown M&M’s. To perform your own Chi-Square test in Minitab, use Stat > Tables > Chi-Square Goodness-of-Fit Test (One Variable).
This example was done with the typical multi-color bag of M&M’s, but it could certainly be done with your bag of festive white, pink, and red M&M’s for V-Day!
Do enough M&M’s have the “m”?
M&M’s are easily identified by the signature “m” printed on each piece of candy. It must pose a quite challenge to stamp the familiar symbol on a surface as uneven as a peanut M&M. It’s not surprising to see that sometimes this “m” is not perfectly printed.
Suppose there is a requirement that no more than 15% of M&M’s have a misprinted “m.” If we count the total number of M&M’s and the number with misprints, we can conduct a 1 proportion test (Stat > Basic Statistics > 1 Proportion):
Of the 622 M&M’s we evaluated (what can I say – we really like M&M’s!), 87 had misprints. Using a 1 proportion test and an alternative hypothesis of greater than 15%, we get at p-value of 0.776. Because the p-value is greater than an α equal to 0.05, we can conclude that the proportion of misprinted M&M’s is 15% or less.
What else can you find out about your bag of M&Ms?
There are many other analyses you could perform on your M&M’s! Let us know in the comments what else you find out about your candy.
For more, check out this special Valentine’s trick to impress your favorite quality engineer: http://blog.minitab.com/blog/real-world-quality-improvement/valentines-day-statistics and this teaching resource that explores more ways to learn statistics with M&M’s.