Workshop Statistics: Discovery with Data, Fourth Edition

TOPIC 20

Tests of Significance: Means

The golden ratio is a famous number not only in mathematics but also in art, music, and architecture. It has been suggested since ancient times that rectangles for which the ratio of width to length equals this golden value are aesthetically pleasing. In this topic, you will investigate whether or not beaded artwork of Shoshoni Indians appears to adhere to this famous number. Other questions that you will investigate include these: Do Cal Poly students tend to follow recommended practices of carrying less than 10% of their bodyweight in their backpacks? Do college students tend to get the recommended eight hours of sleep per night? Do schoolchildren watch more than two hours of television per day on average?

Overview

In the last topic, you studied confidence intervals for a population mean. Now you will turn to the other major type of statistical inference procedure, tests of significance, and apply these procedures to quantitative data and, therefore, a population mean. This procedure will lead you to one of the most famous of statistical techniques: the t-test.

Preliminaries

1. Guess how many points are scored (by the two teams combined) in a typical professional basketball game. (Exercise 20-9)
2. If you are looking to find evidence that rule changes have increased basketball scoring from the previous season, do you think that a sample of one day's games or a sample of one week's games would be more informative? (Exercise 20-9)

Collect Data ...