Confidence intervals and football wins: In an exercise in Chapter 7, we asked wh

Question

Confidence intervals and football wins: In an exercise in Chapter 7, we asked whether college football teams tend to be more likely or less likely to be mismatched in the upper National Collegiate Athletic Association (NCAA) divisions. During one week of a football season, the population of 53 Football Bowl Subdivision (FBS) games had a mean spread (winning score minus losing score) of 16.189, with a standard deviation of 12.128. We took a sample of 4 games that were played that week in the next-highest league, the Football Championship Subdivision (FCS), to see if the spread were different; one of the many leagues within FCS, the Patriot League, played 4 games that weekend. Their mean was 8.75.

Confidence intervals and football wins(continued) Using the football data presented in exercise 8.49, practice evaluating data using confidence intervals.:a. compute the 80% confidence interval. b. How do the conclusion and the confidence interval change as you move from 95% confidence to 80% confidence? c. Why don't we talk about having 100% confidence?

Explanation / Answer

a. ?1 - ?2 = (M1 - M2) = 7.439, 80% CI [-0.604, 15.482].

You can be 80% confident that the difference between your two population means (?1 - ?2) lies between -0.604 and 15.482.

b. ?1 - ?2 = (M1 - M2) = 7.439, 95% CI [-4.98726, 19.86526].

You can be 95% confident that the difference between your two population means (?1 - ?2) lies between -4.98726 and 19.86526.

c. We cannot talk about having 100% confidence because some error is always expected. We cannot say with absolute certainty that if we repeated the survey we would get the same results every time.

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