Players Independent random samples of professional football and basketball players gave the following information (References: Sports Encyclopedia of Pro Football and Official NBA Basketball Encyclopedia). Note: These data are also available for download at the Online Study Center. Assume that the weight distributions are mound-shaped and symmetric.
Weights (in lb) of pro football players: x1; n1 =21
245 262 255 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 270
Weights (in lb) of pro basketball players: x2; n2=19
205 200 220 210 191 215 221 216 228 207 225 208 195 191 207 196 181 193 201
(a) Use a calculator with mean and standard deviation keys to verify that x1 < 259.6,="" s1="">< 12.1,="" x2="">< 205.8,="" and="" s2=""><>
(b) Let u1 be the population mean for x1 and let u2 be the population mean for x2. Find a 99% confidence interval for u1-u2.
(c) Interpretation Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, do professional football players tend to have a higher population mean weight than professional basketball players?
(d) Which distribution (standard normal or Student’s t) did you use? Why?