In this course we will use current events and personal experiences to examine various statistical and probabilistic concepts. By the end of the course, you will be expected to be able to critically analyze the statistics you come across in your day-to-day life and understand how they may have been manipulated. In addition, you will ultimately produce statistical information of your own, complete with analysis.
We may view statistics as the organization and analysis of data. The following quantity would be an example of a statistic: The percentage of people in the US who own a pinball machine. There are several useful statistics which we will explore in this course including the average, the standard error, and the correlation coefficient. Sometimes a statistic is best understood with a picture as opposed to a number and we will study such visual aids including the histogram, the scatter plot, and the regression line.
Probability we may view as an attempt to understand randomness. For example with probability one might try and make sense of the following question: If you chose a person in the US at random, what is the chance that they own a pinball machine? We will explore several probabilistic concepts including that of a model, the expected value, the variance, a confidence interval, and the fundamental mysteries of probability; along with certain explicit models including the binomial model and the models which arise in various gambling situations.
Many of the issues explored in the Chance course will lie at the intersection of statistics and probability. For example you might interview 1,000 US citizens and ask them "Do you own a pinball machine?" and then collect the following statistic: the percentage of these 1,000 people who own a pinball machine. Suppose 8% of those interviewed answered yes. With what right do you have to claim that 8% of the US population owns a pinball machine? To answer this one has to understand how to give a statistics meaning with probability, and this can be quite a tricky business. Often in your life information in this form has been presented to you and it is likely that have and will make decisions based on such information. The primary goal of this course to be able to better understand such information, which will hopefully allow you to make better educated decisions in situations where statistics arise.