Over the years, there have been countless debates about how to fairly determine the winner of a football game that is tied at the end of regulation play. Different sets of rules have been tried across leagues and across time periods, but most have involved starting overtime play with a coin toss. Under a fair rule system, winning the coin toss would not affect the probability of winning the game.

The article "The NFL's Overtime Rules Aren't Fair—But Neither Are the Alternatives".† references data for 82 National Football League (NFL) games that went to overtime between 2012 and 2017. The same article also referenced data from a rule system that was used by the National Collegiate Athletic Association (NCAA) between 1995 and 2006. Under those rules, the team that won the coin flip went on to win in 180 out of 328 games.

(a)

Assume that the sample is representative of all college football games that could be played under this rule system. Is there convincing evidence that winning the coin toss is an advantage? Test the relevant hypotheses using a significance level of ???? = 0.05. (Let p be the population proportion of times the team that wins the coin flip goes on the win the game. Enter != for ≠ as needed.)

H₀:

H_a:

Find the test statistic. (Round your answer to two decimal places.)

Use technology to find the P-value. (Round your answer to four decimal places.)

P-value =

State the conclusion in the problem context.

Reject H₀. We do not have convincing evidence that winning the coin toss is an advantage.Reject H₀. We have convincing evidence that winning the coin toss is an advantage. Fail to reject H₀. We have convincing evidence that winning the coin toss is an advantage.Fail to reject H₀. We do not have convincing evidence that winning the coin toss is an advantage.

(b)

The article reported that 45 out of 82 NFL games that went to overtime between 2012 and 2017 were won by the team that won the overtime coin flip. Observe that the sample proportion for the NFL data from 2012 to 2017 is 0.55. Additionally, it can be shown that the P-value associated with testing the hypothesis that winning the overtime coin flip provides an advantage is 0.1885. The sample proportion (p̂) calculated in part (a) is very similar to the value given in Example 10.12, but the P-value is quite different. Explain how this is possible.

The sample size appears in the ---Select--- numerator denominator of the standard error formula. This results in a ---Select--- larger smaller standard error for the data set with the larger sample size, which results in a ---Select--- larger smaller test statistic and a ---Select--- larger smaller P-value.

(c)

Based on the results of the hypothesis test in Part (a), is it appropriate to conclude that winning the coin toss provides a large advantage?

No. Since the hypothesis test failed to reject the null hypothesis we do not have convincing evidence that winning coin toss provides an advantage.Yes. Since the hypothesis test failed to reject the null hypothesis we can definitively conclude that winning coin toss provides an advantage. Yes. Since the hypothesis test rejected the null hypothesis we can definitively conclude that winning coin toss provides an advantage.No. Since the hypothesis test rejected the null hypothesis we do not have convincing evidence that winning coin toss does not provide an advantage.No. The hypothesis test may have rejected the null hypothesis, but there is a chance that our test made a mistake so we cannot definitively conclude that winning the coin toss provides an advantage.

(d)

Calculate a 90% confidence interval to estimate the long-run proportion of games that would be won by the team that won the coin toss under this rule system. (Enter your answer using interval notation. Round your answer to four decimal places.)