Question

Before the overtime rule in the National Football League was changed in 2011, among 460 overtime games, 252 were won by the team that won the coin toss at the beginning of overtime. Using a 0.05 significance level, test the claim that the coin toss is fair in the sense that neither team has an advantage by winning it. Does the coin toss appear to be fair?

Answer 1

Solution:

The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

Where:

Now the p-value is:

Using the standard normal table, we have:

Since the p-value is less than the significance level, we, therefore, reject the null hypothesis and conclude that the coni toss does not appear to be fair.