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# Determining the Validity of Sample Size

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Source:
Author: Bob Bonnet and Dan Keen

### Overview

A lot of investigating can be done with several bags of M&M's candies! And when you finish your investigations, you can eat them! (But, do not eat them if you are allergic to chocolate or can't tolerate sugar!)

Just think of all the questions you can pose:

• How many blue candies are in a bag of M&M's?
• What percentage of each color is in a bag?
• Are the same number of each colored candy found in each bag, or are their quantities random?
• Can you predict how many of each color will be in a bag before it is opened? (You can if the colors are not random.)
• Some people believe there are always more brown candies than any other color. Is this true?
•  Does each bag contain exactly the same number of candies?
• Does each candy weigh the same, or are some bigger than others?

Maybe you should eat a few candies before exploring the answers to these questions, just to be sure you have plenty of energy!

### Hypothesis

Hypothesize that four bags constitute a large-enough sample size to know whether or not you can predict how many of each color candy will be in a bag before it is opened.

### Materials' List

• Four bags of M&M's candies
• Gram weight scale
• Coat hanger
• Three paper clips
• Piece of string
• Use of a doorjam

### Procedure

Purchase four bags of M&M's candies (or similar bags of multicolored candies). With a pencil and paper, draw a table with column headings for BAG #1, BAG #2, and BAG #3. The number of each colored candy will be recorded under each bag. If you know how to use a spreadsheet program on a computer, set up the table on the spreadsheet.

Open a bag of M&M's candies. Count the number of each colored candy, and write the number down on the table under the column labeled BAG #1.

In the same way, open a second bag, count and write down the number of each color under the BAG #2 heading. Finally, do the same with the third bag. Add each column and write down the total number of candies in each bag.

Looking at your table of data, you can now answer all the questions we posed.

• Percent—Percentage is a measure of a part of something to the whole thing. It is expressed in hundredths. Percent comes from the Latin words per meaning by, and centum meaning one hundred. The symbol for percent is %. To find the percent, divide the part by the whole, and then multiply by 100.

For example, suppose 13 green candies are in a bag, and the total number of candies in that bag is 58.

Find the percentage of each colored candy to the total number of candies in the bag. Do this for each of the three sample bags, and write this figure on your table.

• Sample Size—Scientists often use the concept of sample size to learn what a large group might be like based on data gathered from a small group. The size of the sample group should be big enough to give a true picture of the larger group.

Is the data you gathered by only evaluating three bags accurate enough so you can make statements that are true of every bag of M&M's candy?

If you found that the number of each colored candy is very different in each of the three bags, would you then predict that when you open a fourth bag, the number of colored candies will also be random in that bag?

What was the total number of candies in each bag? Was it always the same? Is there a range? For example, if one bag had 55, one 58, and one 57, then the range of candies is from 55 to 58. By your examination of three bags of candy, would you predict that every bag you open in the future will not contain exactly the same number of candies?

• Weight Comparison—On the label of the candy bag is the weight of its contents. In the case of an M&M's bag, 47.9 grams. But, did you find each bag had a different number of candies? What can this mean? Either the weight shown on the label is only an approximate or minimum weight, or each candy does not weigh exactly the same!

Set several candies next to each other. Do they all look the same size or are some bigger than others?

If you have access to a very accurate gram weight scale at school, weigh two bags and compare their weight.

You can also build a simple balance beam to compare the weight of two bags. Use a coat hanger suspended from a door jam with a candy bag hanging from each end to see if they are in balance (the hanger will tilt if one bag is heavier than the other).

### Results

Write down the results of your experiment. Document the data collected.

### Conclusion

Come to a conclusion as to whether or not your hypothesis was correct.

Something More

Determine unit cost. If a bag of candy costs 60 cents and it contains 55 candies, how much does each individual candy cost? This is called unit cost. Divide the total cost (60 cents) by the total number of candies (55):

How much does each candy cost in a bag that contains 58 candies? Did you get more candies for your money?