Independent random samples of professional football and basketball players gave
ID: 3246905 • Letter: I
Question
Independent random samples of professional football and basketball players gave the following information. Assume that the weight distributions are mound-shaped and symmetric.
Weights (in lb) of pro football players: x1; n1 = 21
Weights (in lb) of pro basketball players: x2; n2 = 19
(a) Use a calculator with mean and standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to one decimal place.)
(b) Let 1 be the population mean for x1 and let 2 be the population mean for x2. Find a 99% confidence interval for 1 2. (Round your answers to one decimal place.)
Explanation / Answer
(a)
(b) First we have to find mean difference for 1 2 = 259.67 - 205.89 = 53.8
pooled variance sp2 = [(n1 -1)s12 + (n2 -1)s22] / (n1 + n2 -2) = (20 * 11.962 + 18 * 12.982 )/ 38 = 155.09155
sp = 12.5
so 99% confidence interval = (1 2) +- t38, 001 sp sqrt [1/n1 + 1/n2 ]
= 53.78 +- 2.7116 * (12.454) * sqrt (1/20 + 1/18)
= 53.78 +- 2.7116 * 12.454 * 0.3249
= (42.8, 64.8)
x1 = 259.7 s1 = 12.0 x2 = 205.9 s2 = 13.0