M & M Project

Purpose:To see the variety of confidence intervals produced from a mix of samples, and to eat some chocolate.

Knowledge:Given data, make a confidence interval for proportions, using a calculator command.

Skills:This assignment will help you to practice the vocabulary and interpretations connected to confidence intervals of proportions.

Task:Let's work to answer a very important question, vexing humankind for decades:How are the colors distributed in the bags of M & Ms????Is the company reporting accurate color percentages for their product? This activity will guide you through constructing a confidence interval for the proportion of M&M's in a particular color. You will compare your confidence interval to those of your classmates and see what percent of them actually contain the proportion reported by the manufacturer.

M&M says:

On average, our mix of colors for M&M'S CHOCOLATE CANDIES is:

M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown.

Each large production batch is blended to those ratios and mixed thoroughly. However, since the individual packages are filled by weight on high-speed equipment, and not by count, it is possible to have an unusual color distribution.

(already answered) 1.Treat your bag of M&M's as a simple random sample and:

a.Count the following --

Number of RED M&M's: 22

Total number of M&M's: 58

Proportion of RED M&M's: 22/58= 0.3793

b.See if the requirements for constructing a confidence interval for proportions are satisfied. Show your work here for n*p*(1-p)[Note - the "p" is the 0.13 that is the expected proportion of RED]:

c.The conditions might not be satisfied, depending on how many candies were in your bag.If the conditions are not met, what could you do? (noteAnswer this even if you found the condition met in your case.Just say what you would do)

(already answered) d.Construct a 95% confidence interval for the proportion of RED M&M's using your data (not using any classmate data yet).Feel free to use the calculator's Interval command. Be sure to include an interpretation of your interval.

My interval: (0.25444, 0.50418)

e.Below, draw a number line with your and groupmates intervals

intervals: (0.25444, 0.50418),(.0767, .27418), (0.03838, 0.21162),(0.0040, 0.1012), (0.119, 0.273), (0.05228, 0.23863)

number line:

3. According to Mars, Inc., M&M's are 13% red.

a.What percent of the group's confidence intervals contained the true proportion of RED M&M's? (in other words, what proportion of the intervals had 0.13 within the interval?)

b.What how many of the confidence intervals would you mathematically expect to contain the true proportion, assuming you had 100 people in your group?Explain.

4. a.If you had a larger sample of M&Ms, how would you expect the confidence interval to be affected?

(already answered) b.All group members should have already posted their count of M&Ms on the discussion page.So now you can pool the data from your group and assume that all the M&M's constitute one large sample of M & M's.

Total number of M&M's for entire group: 70

Total number of REDs for the entire group: 385

Proportion of Red M&M's for the entire group: 70/385=0.1818

(already answered) c.Construct a 95% confidence interval for the proportion of Red M&M's based on the pooled group data.

Group interval: (0.14329, 0.22034)

d.Does this confidence interval contain the true proportion of Red M&M's as reported by Mars?

e.How does the margin of error for this group confidence interval compare to the margin of error for your individual confidence interval? Compute both, showing your work, and compare.A quick method of getting the error when you have the interval is (upper - lower)/2

f.Do you trust the percentages of the colors reported by the M & M company?(say yes or no, and give mathematical evidence for your answer)