Sampling Reese’s Pieces

Pre Lab

A technique called sampling is sometimes used to estimate population size. In this procedure, the organisms in a few small areas are counted and projected to the entire area. For instance, if a biologist counts 10 squirrels living in a 200 square foot area, she could predict that there are 100 squirrels living in a 2000 square foot area.

  1. A biologist collected 1 gallon of pond water and counted 50 paramecium. Based on the sampling technique, how many paramecium could be found in the pond if the pond were 1,000 gallons?
  1. What are some problems with this technique? What could affect its accuracy?

Experiment

This lab is going to look at random sampling with Reese’s Pieces and test to see if random sampling is a reliable means of looking at a whole population.

  1. Reese’s Pieces candies have three colors: orange, brown, and yellow. Which color do you think has more candies in a package: orange, brown or yellow?
  1. Guess the proportion of each color in a bag:

Orange____ Brown____ Yellow____

  1. If each student in the class takes a sample of 25 Reese’s pieces, would you expect every student to have the same number of orange candies in their sample? Explain.
  1. Pretend that 10 students each took samples of 25 Reese’s pieces. Write down the number of orange candies you might expect for these 10 samples:

______

These numbers represent the variability you would expect to see in the number of orange candies in 10 samples of 25 pieces.

  1. You will be given a cup that is a random sample of Reese’s pieces. Close your eyes, and count out 25 candies from this cup. After you have 25 candies, open your eyes. Now, count the colors for your sample and fill in the chart below:

Orange YellowBrown

Number of candies______

Proportion of candies______

  1. Total the number of each color candy for the people at your table.

Orange YellowBrown

Number of candies______

Proportion of candies______

  1. Write the number AND the proportion of orange candies in your sample on the board.

Record the total class data below:

Orange YellowBrown

Number of candies______

Proportion of candies______

Questions

The proportions are the sample statistics. For example, the proportion of orange candies in your sample is the statistic that summarizes your sample.

  1. How does your actual sample values compare to the ones you estimated in question 2?
  1. How does your proportion of each color candy relate to your table’s proportion of each color? How does your table’s proportion of each color candy relate to the whole class data?
  1. According to individuals who make a hobby out of counting Reese’s Pieces, the average bag contains 45% orange candies. How does your sample compare to this statistic? How does your table sample compare? How does the whole class data compare? Explain your observations.
  1. How many Reese’s pieces do you think you have to count to get a valid representation of the entire population? Explain your reasoning.
  1. Calculate percent error for each of your data sets (individual, table, and whole class). Which data set was most accurate? (Show your work!)

Percent Error = l observed – expected l x 100%

expected