Reese's Pieces Discussion - Instructions 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. 1. Physical Sample: Reese's Pieces come in three colors: orange, brown and yellow. Buy a small bag of Reese's Pieces, take a random sample of 25 of the candies, and record the number and proportion of orange candies in your sample. 2. Think about the following questions. You should be able to answer each of these. Is the proportion of orange candies among the 25 you selected a parameter or a statistic? Is the proportion of orange candies manufactured by Hershey's process a parameter or a statistic? What is your best estimate (based on your sample) of the true population proportion? Do you suspect that every person in the class obtained the same proportion of orange candies in their sample? If everyone in the class estimates the population proportion of orange candies with the proportion of orange candies in their sample, will everyone have the same estimate? 3. Virtual Sample: Now I want you to take many random samples of Reese's Pieces. Since it would be expensive, time-consuming, and possibly fattening to choose many real samples of Reese's Pieces, I want you to use a Java applet to simulate this process. Go to this site and answer the following questions, so you can discuss the results you get. Go to http://www.rossmanchance.com/applets/OneProp/OneProp.htm?candy=1 Set "Probability of orange" to .45, "Number of candies" to 25, "Number of samples" to 1, and click on Proportion of orange. Then click Draw Samples. Watch the applet draw one sample of 25 virtual Reese's Pieces. Below, it plots the proportion of orange pieces in its virtual sample. Now change "Number of samples" to 500 and uncheck the Animate box, then Draw Samples. What do you notice about the graph? Click on Summary Stats to display the mean and standard deviation of your sample proportions. Record the mean and standard deviation of your sample proportions, and any observations you have about the graph. Now draw 500 samples of 75 candies each. Now what do you notice about the graph? How did the graph change when your sample size increased? Record the mean and standard deviation of these sample proportions, and any observations you have about the graphs and how they're alike or different