M&Ms Lab: Inferences for One Population

Summary: In this lab you’ll do two kinds of inferences: population mean for numeric data and population proportion for binomial data.

  The first population is Fun Size plain M&Ms packages; you will test and estimate the mean number of candies in a package. But first, how many M&Ms do you think the average Fun Size package holds? Write your answer in the box at right.

The second population is individual plain M&Ms. The “Model” column of the table below shows the distribution of colors that used to be listed on the company Web site. In this lab you’ll test just the proportion of oranges; in Chapter 12 you’ll learn to test the whole model.

Collect Data

Each team takes four Fun Size packs, one data sheet per person, and one extra data sheet. Please record all data on all sheets. Each team will turn in the extra sheet at the end of class, and I’ll collate the whole class’s data.

Count the candies of each color from the first package, record the numbers in the first column of the table, and enter the total. Count the candies in the bag and verify that it matches your column total. Save the package (uneaten) in case you have to do a recount.

Repeat for the other three packages in turn.

Then add across to put the total number of each color and total number of candies in all bags in the Total column. Verify that the grand total is correct both across and down.

Finally, use the Total column to compute a point estimate for the percentage of each color. Verify that your proportions add to 1, give or take a bit of rounding.

You may now eat the data.

Activities (do either A/D/E or B/C/E)

Do these on separate paper. It’s okay to collaborate with your teammate, but make sure you each do all the TI-83 calculations and compare your results. You’re not handing this in, but I will look at your work. Here’s your chance to practice for quizzes: show your work including TI-83 inputs and outputs, number the steps of hypothesis tests, phrase conclusions properly, and so forth.

Later, we’ll consolidate sample data from the whole class and do more tests.

Activity A: Hypothesis Test for a Mean

Use your data to test the claim “the average number of M&Ms in a Fun Size package equals” (your estimate from page 1). (Different team members might not all have the same hypothesis.) Choose the most appropriate significance level out of 0.05, 0.01, and 0.001.

Activity B: Confidence Interval for a Mean

Estimate the average number of M&Ms in a Fun Size package, with 95% confidence. (See the Caution for Activity A.) Give your answer as a range.

Activity C: Hypothesis Test for a Proportion

Test the hypothesis “Fun Size M&Ms are 20% orange.” Choose the most appropriate significance level out of 0.05, 0.01, and 0.001. (Treat the candies from all four bags as a consolidated sample.)

Activity D: Confidence Interval for a Proportion

Construct a 95% confidence interval for the proportion of orange in plain M&Ms. Give your answer as a range.

Activity E: Sample Size for a Proportion

Your margin of error for the previous activity was quite large. How many M&Ms would you need in a sample to determine the proportion of orange with a margin of error of ±2% in a 95% CI? (Hint: the answer 2401 is way too big.)