In analyzing data from over 700 games in the National Football League, economist David Romer identified 1068 fourth-down situations in which, based on his analysis, the right call would have been to go for it and not to punt. Nonetheless, in 959 of those situations, the teams punted. Our goal is to find a 99% confidence interval for the proportion of times NFL teams punt on a fourth down when, statistically speaking, they shouldn’t be punting.1 Assume the sample is reasonably representative of all such fourth down situations in the NFL.
The standard error of the sample statistic in this situation is 0.009.
1Moskowitz, T. and Wertheim, J., Scorecasting, Crown Archetype, New York, 2011, p. 39.
What is the sample statistic? Round your answer to two decimal places.
Which distribution should we use when finding the multiplier?
The t-distribution with 958 degrees of freedom
The t-distribution with 1067 degrees of freedom
The standard normal distribution
The t-distribution with 699 degrees of freedom