Question: Economics and Finance The U.S. Bureau of Engraving and Printing produces $1, $5, $10, $20, $50, and $100 bills. The $2 banknote is still legal tender but is currently not in production. Each bill is designed to have the same width, but many people perceive larger-denomination bills to be larger in size. Independent random samples of newly minted $1 and $20 bills were obtained, and the width of each (in mm) was recorded. The summary statistics are given in the following table.
Assume the underlying distributions are normal.
a. If the population variances are assumed equal, is there any evidence to suggest the mean width of a $20 bill is greater than the mean width of a $1 bill? Use a = 0.01.
b. If the population variances are assumed unequal, is there any evidence to suggest the mean width of a $20 bill is greater than the mean width of a $1 bill? Use a = 0.01.
c. Why do both tests lead to the same conclusion (with very similar p values)?