Independent random samples of professional football and basketball players gave

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)

x1 = 259.7

s1 = 12.3

x2 = 205.9

s2 = 12.6

b)CI [51.348, 56.252].

1 - 2 = (M1 - M2) = 53.8, 99%

Pooled Variance
s2p = (SS1 + SS2) / (df1 + df2) = 310.05 / 38 = 8.16

Standard Error
s(M1 - M2) = ((s2p/n1) + (s2p/n2)) = ((8.16/21) + (8.16/19)) = 0.9

Confidence Interval
1 - 2 = (M1 - M2) ± ts(M1 - M2) = 53.8 ± (2.71 * 0.9) = 53.8 ± 2.452

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