Question # a) What is the standard deviation of the distribution of x? b) What is the standard deviation of the distribution of x - y ?

Describing quantitative data
ANSWERED In Major League baseball, do Left-Handed hitters and Right-Handed hitters tend to have different batting averages? We will study this question by taking random samples of m=45 seasonal batting averages from left-handed batters and n=53 seasonal batting averages from right-handed batters. The mean batting averages were x= .256 for the left-handers and y=.254 for the right-handers. It is recognized that the true standard deviations of batting averages are σx = .0324 for left-handed batters and σy = .0298 for right-handed batters. The true (unknown) mean batting average for left-handers = μx , while the true unknown mean batting average for right-handers = μy . We would like to examine μx − μy . a) What is the standard deviation of the distribution of x? b) What is the standard deviation of the distribution of x - y ? c) Create a 98% confidence interval for μx − μy ? leftparen1.gif , rightparen1.gif d) What is the length of the confidence interval in part c) ? 