• Write a null and alternative hypothesis for a hypothesis test.
• Decide if a sample statistic provides enough evidence to reject the null hypothesis.

Is it fair?

Recall the scenario: Suppose that you are playing a game with your friend that involves flipping a coin. Each round consists of flipping the coin [latex]10[/latex] times. In one round of play, your friend gets [latex]8[/latex] heads out of the [latex]10[/latex] total flips.

Your friend claims the coin is fair, but you aren’t convinced. You can’t prove for certain that your friend’s coin is weighted unfairly (without special equipment, of course), but you can test your hypotheses with a sample of coin flips.

The statistical evidence, often represented by the P-value, is used to determine the strength of the evidence against the null hypothesis. The P-value represents the probability of obtaining the observed data, or more extreme data, under the assumption that the null hypothesis is true.

• The smaller the probability, the more unlikely it is to observe the sample data given that the null hypothesis is true.
• The larger the probability, the more likely it is to observe the sample data.

If the proportion of heads in your sample is high enough, it provides strong evidence that your friend’s coin is weighted in their favor. In other words, a high enough proportion of heads would be sufficient evidence for you to reject the assumption that your friend’s coin is fair.

Let’s suppose that you flip the coin [latex]20[/latex] times for your sample.