Workshop Statistics: Discovery with Data, Fourth Edition

TOPIC 13

Sampling Distributions: Proportions

Reese's Pieces candies come in three colors: orange, brown, and yellow. If you repeatedly take random samples of 25 candies, do you expect the proportion of orange to be the same every time, or do you expect to see variability in those sample proportions? If these sample proportions show variability, how much will they vary? Most importantly, will the sample proportions display any predictable pattern in how they vary? This same issue arises in more important contexts as well. For example, when a polling organization asks a random sample of people whom they intend to vote for, how much variability can be expected in the sample proportion who plan to vote for your favorite candidate? Will this allow you to accurately predict the eventual winner? If a predictable pattern really does emerge, then that pattern could enable you to anticipate how close the sample result is likely to be to the proportion for the actual population. You will explore these issues in this topic as you begin to study the important topic of sampling distributions.

Overview

You have been studying the ideas of probability and normal distributions. These ideas arise in the practice of statistics because (as you studied in Topics 4 and 5) proper data collection strategies involve the deliberate introduction of randomness into the process. Therefore, drawing meaningful conclusions from sample data requires an understanding of the properties of randomness. In this topic, ...