We would like to know if there is a difference in how far men and women of the same height can jump. We recruit 39 men and 43 women for this study. Everyone in the study is 5 feet 11 inches. We then ask them to run 10 feet to the edge of a sandpit and then jump as far as they can into the sand. Distance is measured from the edge of the pit to the point where their feet first hit the sand. The men in this study jumped an average of 183 inches (15 feet 3 inches) with a sample standard deviation of 4 inches. The women in this study jumped an average of 179 inches (14 feet 11 inches) with a sample standard deviation of 2 inches. 1) What is a 80% confidence interval for the true difference in mean jump distances of men and women? Interpret this in the context of the problem.
2) What is a 95% confidence interval for the true difference in mean jump distances of men and women? Interpret this in the context of the problem.
3) Is the interval in part (b) wider or narrower than the interval in (a)? Why might that be?