In: Statistics and Probability
Consider researching the maximum distance that prospective professional quarterbacks can throw a football. Suppose that 41 NFL draft prospect quarterbacks were asked to throw a football as far as they could. For this sample, the mean distance was 68.9 yards and the sample standard deviation was 5.2 yards. Find a 90% confidence interval for the true mean maximum distance that the population of NFL prospect quarterbacks can throw a ball. Also, find a 90% confidence interval for the true population standard deviation of distances. Suppose professional blowhard Skip Bayless claimed the true mean distance was less than 70 yards. Use a hypothesis test (with significance level 0.05) to determine whether we can conclude that Bayless's claim is accurate, based on these data.