Topic: 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...

Section one only


Topic: 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) 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? Part 2 Class data from Part 1 of the Reese’s Pieces Lab. 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 http://www.rossmanchance.com/applets/OneProp/OneProp.htm?candy=1) m) In what way would the dotplot have looked different if each student had taken a sample of 75 candies instead of 25?