568 words - 3 pages

M&M Project

Math 336

(1) Buy a packet of regular size M&M's. Record the frequency of each color and then transfer this information to a bar chart and a pie chart.

(2) Represent the number of M&M's per packet on a histogram using all of the class data. Is your histogram normally distributed? Check using the empirical rule. Also choose your favorite color and draw a histogram of the number of M&M’s of that color per packet based on class data. Draw a box-plot of the total number of data in a packet based on class data.

(3) There are numerous hypothesis tests that can be done. Obtain the mean number of M&M's per packet for the whole class. Consider as a null hypothesize that the actual number of M&M's in your packet is the ...view middle of the document...

(6) Another obvious test would be to test the proportion of colors present. Intuitively, we might expect each color to occur with the same probability p (Null Hypothesis) but a quick inspection of data suggests this is not so. Test this hypothesis.

(5) Perhaps the manufacturers do not stick to any rule when it comes to color distribution, although they claim otherwise. Construct a test with the assumption that the Mar’s Company has a color code distribution (Null Hypothesis). In the event that the hypothesis is true, what is the approximate distribution for M&M colors based on your test.

(6) This test can be further modified. Do you think that our intuitive assumption is reasonable? Maybe, every color was not meant to be in the same proportion. To find a reasonable set of proportions that would correspond to the true colors, calculate a posterior probability for each color (choose two) based on your assumptions in part (4), by using a Bayesian model based on 11 increments given by : 0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1.

(7) Repeat the same question but now use a beta function for each color of your two chosen colors.

(8) The Mars company which makes M&M's claim that "candies contain 30% browns, 20% each of yellows and reds and 10% each of oranges, greens and blues". Test this hypothesis using all of the class data. Is this substantially different to the null hypothesis in (5) above?

(9) Find the confidence intervals at the 90% and 95% confidence levels for the estimate of the true mean number of M&M's in a packet using all of the class data.

(10) Formulate a null hypothesis for the value of the standard deviation in the mean number of M&M's per packet. Can you think of an appropriate test to see if your hypothesis is true?

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