# 5.6.1 - Example: Game of Life

5.6.1 - Example: Game of LifeA family is playing The Game of Life. This is a board game with a plastic spinner in the center. The spinner has 10 slots. The player who is the police officer collects \$5,000 every time a player spins a 10. Mom has been the police officer for the majority of the game and only twice has a player spun a 10! She wants to test if the spinner is fair. If the spinner is fair then it should result in a 10 in 10% of spins (i.e., \(p=\frac{1}{10}\)). While Mom was the police officer the wheel was spun 52 times. In those 52 spins, 2 were 10s for a sample proportion of \(\widehat{p}=\frac{2}{52}=0.038\).

Let's use the information in this scenario to determine if there is evidence that the spinner is unfair (i.e., \(p \ne 0.10\)).

If the spinner is fair then \(p=0.10\). This statement include an equality so this is our null hypothesis. Our alternative hypothesis is that the spinner is not fair.

\(H_0: p=0.10\)

\(H_a: p \ne 0.10\)