How are a Sample and the Population Related?

A population parameter is a number that describes some characteristic of a given population, which, in statistics, is the entire group of individuals about which we want information. The population parameter is a constant value that does not change. Many times it is impractical or even impossible to calculate the population parameter of interest, the most common reason being that populations are often composed of very large numbers of individuals. When we cannot calculate the population parameter directly, we use a sample, which is a part of the population from which we actually collect information. From the sample we calculate a statistic, which is a number that describes some characteristic of the sample. A statistic will vary depending on the sample from which it was calculated.

How are a sample and the population related? We use information from a sample (a statistic) to draw conclusions about a population parameter. We will use this relationship while performing the following investigation.

Problem:
Mars, Incorporated claims that when producing milk chocolate M&M’S®, 17% of the total number produced are green in color.

Question of Interest:
Is the claim that 17% of milk chocolate M&M’S® produced by Mars, Inc. are green a valid claim?

Instructions:
Answer the following question's using your "package" of M&Ms.  

If you'd like, you can also get a real regular size bag of plain M&Ms (the brown packaging) and have a snack while you work! :)

STEP 1 (answer pre-M&Ms PDF):

1) What is the specific question that needs to be addressed in your investigation?

2) How does this question relate to the background information above?

3) What is the population of interest in the investigation?

4) What is the population parameter of interest in the investigation?

5) Why can we not realistically calculate the population parameter of interest directly?


STEP 2 (Perform the following investigation using your PDF sample of M&M’S): 

1) Count the number of M&M’S® on your first sheet - aka your sample. The total number of M&M’S® in one sample/your one sheet is __________________________ .

2) Calculate the proportion of green M&M’S® in the sample. The proportion of green M&M’S® is __________________________ .

3) Give an estimate for the proportion (percentage) of green M&Ms that Mars, Inc. makes in the entire M&M population based on your sample.

4) Combine your sample sheet with a classmate and repeat steps 1-3.