Topic: Confidence Intervals for Proportions Activity: Reese's Pieces

Background Information: The goal of a confidence interval is to estimate a population parameter based on a sample statistic. All confidence intervals have the form: point estimate margin-of-error.

Part 1

Example 1: Colors of Reese's Pieces Consider the population of the Reese's Pieces candies manufactured by Hershey. Suppose that you want to learn about the distribution of colors of these candies but that you can only afford to take a sample of 25 candies.

a)Take a random sample of 25 candies and record the number and proportion of each color in your sample. (Use this applet to get your sample http://www.rossmanchance.com/applets/OneProp/OneProp.htm?candy=1 )

Orange Yellow Brown

Number

Proportion

b)Is the proportion of orange candies among the 25 that you selected a parameter or a statistic?

c)Is the proportion of orange candies manufactured by Hershey's process a parameter or a statistic? What symbol represents it?

d)Do you know the value of the proportion of orange candies manufactured by Hershey?

e)Do you know the value of the proportion of orange candies among the 25 that you selected?

f)Do you suspect that every student in the class obtained the same proportion of orange candies in his/her sample?

These simple questions point out the important fact that one typically knows (or can easily calculate) the value of a sample statistic, but only in very rare cases does one know the value of a population parameter. Indeed, a primary goal of sampling is to estimate the value of the parameter based on the statistic.