Question

Who are taller, pro football players or pro basketball players? A random sample 45 pro football players resulted in a mean height of x-6.179 feet. A random sample 40 pro basketball players resulted in a mean height of y-6.453 feet. It is recognized that the true standard deviation of pro football players heights is Ох-0.47 feet while it is recognized that the true standard deviation of pro basketball players heights is ay0.55 feet. The true (unknown) mean of football players heights is Hx feet, while the true (unknown) mean of basketball players heights is y feet. 

Answer 1

a) Variance of Xbar = 6.179/sqrt(45)= 0.92111
b) Variance of Ybar = 6.453/sqrt(40) = 1.02031
c) Variance of Xbar - Ybar = 0.92111+ 1.02031 = 1.94142
d) SD of Xbar - Ybar = 1.39335
e) Z critical value = +/- 1.881

g)

The 94% confidence interval is (6.179 - 6.453) +/- 1.881 * 1.39335 = (-2.89489135,2.34689135)

h)

Test Statistic Z = (6.179-6.453) / 1.39335 = -0.1967

i) P-value = 0.4220

j) P-value = 0.8440