Workshop Statistics: Discovery with Data, Fourth Edition

TOPIC 18

More Inference Considerations

Do one-third of all American households own a pet cat? If not, is the actual proportion close to one-third? If a baseball player improves his batting success rate substantially, or if a new drug succeeds at alleviating pain more often than the standard drug, is a test of significance guaranteed to reveal the improvements? If not, what factors affect how likely the test is to show the improvements? Finally, if an alien landed on Earth and set out to estimate the proportion of human beings who are female, what might the alien do wrong in constructing its confidence interval? In this topic, you will examine such dissimilar, occasionally even silly, questions as you explore some of the finer points of confidence intervals and significance tests.

Overview

In the previous two topics, you explored and applied the two principal techniques of statistical inference: confidence intervals and tests of significance. This topic will give you more experience with applying these procedures, and you will also investigate their properties, including some fairly subtle ones, further. More specifically, you will consider the relationship between intervals and tests, learn to watch for ways in which these techniques are sometimes misapplied, and explore the important concept of power.

Preliminaries

1. Guess what proportion of American households includes a pet cat. (Activity 18-2)
2. If 31.6% of a random sample of American households includes a pet cat, would you be ...