 In Major League baseball, do Left-Handed hitters and Right-Handed hitters tend to have different batting averages? We will study this question by taki Cheyanne Leigh 2021-05-17 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 $$\sigma$$;x = .0324 for left-handed batters and $$\sigma$$;y = .0298 for right-handed batters. The true (unknown) mean batting average for left-handers = $$\mu$$x , while the true unknown mean batting average for right-handers = $$\mu$$y . We would like to examine $$\mu x- \mu y$$ . 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 $$\mu x- \mu y$$? d) What is the length of the confidence interval in part c) ?

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a) 0.0324
b) 0.0063
c) -0.0128,0.0168
d) 0.0296