Workshop Statistics: Discovery with Data, Fourth Edition

TOPIC 17

Tests of Significance: Proportions

How often does the winning team in a baseball game score more runs in one inning than the losing team scores in the entire game? Does this happen three-quarters of the time, as someone once claimed in a letter to the “Ask Marilyn” columnist? In this topic, you will learn to assess the evidence that sample data provide about such a claim. Another example that you will investigate concerns whether or not people who need to make up an answer to a question on the spot tend to select certain answers more than others.

Overview

In the previous topic, you took what you learned about the concept of statistical confidence in Unit 3 and studied a procedure known as confidence intervals. In this topic, you will augment what you learned about the concept of statistical significance by studying a procedure known as a test of significance. Such a procedure assesses the degree to which sample data provide evidence against a particular conjecture about the value of the population parameter of interest. Your understanding of the reasoning process behind these tests will deepen, and you will study the formal structure of a test of significance, while learning a specific procedure for conducting a test concerning a population proportion.

Preliminaries

1. In what percentage of major-league baseball games would you predict that the winning team scores more runs in one inning than the losing team scores in the entire game? (Activity 17-5)
2. Consider a cola taste ...