133% ,a search Independent random samples of professional football and basketbal

Question

133% ,a search 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: x1i n1 21 248 261 254 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 270 Weights (in lb) of pro basketball players: x2i n2 19 204 200 220 210 192 215 222 216 228 207 225 208 195 191 207 196 183 193 201 (a) Calculate the means and standard devlations: X1, S1, 2, and s2. (Round your answers to one decimal place.) X1 X2 S2 (b) Let 1 be the population mean for X1 and let 2 be the population mean for x2. Find a 99% conr den cemerval for 1-2. (Round your answers to one decimal place.) lower limit

Explanation / Answer

a)

x1 = 259.7 (=average(n1,n2,..excel function)

s1 = 11.9 (=Stdev.s(n1,n2,,, excel function)

x2 = 205.9

s1 = 12.7

b) 1 - 2 = (M1 - M2) = 53.8, 99% CI [43.252, 64.348]

Calculation

Pooled Variance
s2p = ((df1)(s21) + (df2)(s22)) / (df1 + df2) = 302.9 / 38 = 150.93

Standard Error
s(M1 - M2) = ((s2p/n1) + (s2p/n2)) = ((150.93/21) + (150.93/19)) = 3.89

Confidence Interval
1 - 2 = (M1 - M2) ± ts(M1 - M2) = 53.8 ± (2.71 * 3.89) = 53.8 ± 10.548

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