On October 5, 2005, a tour boat named the Ethan Allen capsized on Lake George in New York with 47 passengers aboard. In the inquiries that followed, it was suggested that the tour operators should have realized that so many passengers were likely to exceed the weight capacity of the boat. In this topic, you will examine how a sample mean varies, and how this information enables you to address larger issues such as this accusation.
In the previous topic, you studied how a sample proportion, which summarizes the distribution of a categorical variable, varies from sample to sample. In this topic, you will explore how the sample mean, which summarizes the center of the distribution of a quantitative variable, varies from sample to sample. The sampling distribution of the sample mean is a bit more complex than the sampling distribution of the sample proportion, because the shape of the underlying population comes into play—but a variety of similarities between the two sampling distributions emerge. As in the previous topic, you will again find that these statistics do not vary haphazardly but according to a predictable, long-term pattern, and you will see that sample size affects the amount of variation that occurs.