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

Number10105

Proportion0.40.40.2

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

Statistic, because it describes the sample of candies taken from the population.

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

What symbol represents it?

Parameter, because it describes the whole population of candies made by Hershey's. Symbol: P

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

No. That's why the sample proportion is used to estimate the proportion of orange candies made by Hershey's.

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

Yes. p = 0.4

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.

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

No. They will have different proportions.

Part 2

Class data from Part 1 of the Reese's Pieces Lab.

10/2515/2511/2512/2515/25

14/2512/2513/2513/2514/25

17/2514/2512/2515/2510/25

12/259/2513/25

g) Create a dotplot of the class data.

h)Did everyone obtain the same number of orange candies in their samples?

i)If every student was to estimate the population proportion of orange candies by the proportion of orange candies in his/her sample, would everyone arrive at the same estimate?

j)Based on what you have learned about random sampling and having the benefit of seeing the sample results of the entire class, take a guess concerning the population proportion of orange candies.

k)Again assuming that each student had access only to her/his sample, would most estimates be reasonably close to the true parameter value? Would some estimates be way off? Explain.

l)In what way would the dotplot have looked different if each student had taken a sample of 10 candies instead of 25? (If unsure, you can check this using the Reese's Pieces applet found at http://statweb.calpoly.edu/chance/applets/applets.html.)