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4. [10.27 Points] DETAILS BBUNDERSTAT12 7.4.0145. MY NOTES ASK YOURTEACHER PRACTICE ANOTHER 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: 11; n1 = 2'1 243 263 256 251 244 226 240 265 25? 252 282 256 250 261:l 270 275 245 275 253 265 272 Weights (in lb) of pro basketball players: 12; n2 = 19 204 200 220 210 193 215 222 216 228 207 225 208 195 191 20? 196 183 193 201 I USE SALT {a} Use a calculator with mean and standard deviation keys to calculate 1', 5 places.) id: 522' (b) Let #1 be the population mean for x1 and let #2 be the population mean for x2. Find a 99% condence interval for ,Lt1 :42. 1, x2, and 52. (Round your answers to four decimal (Round your answers to one decimal place.) lower limit upperlimit (c) Examine the condence 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? 0 Because the interval contains only negative numbers, we can say that professional football players have a lower mean weight than professional basketball players. 0 Because the interval contains both positive and negative numbers. we cannot say that professional football players have a higher mean weight than professional basketball players. 0 Because the interval contains only positive numbers, we can say that professional football players have a higher mean weight than professional basketball players. (d) Which distribution did you use? Why? 0 The standard normal distribution was used because 0'1 and 02 are known. and 0' are known. 0 The Student's tdistribution was used because 0'1 2 O The standard normal distribution was used because 0'1 and 0'2 are unknown. O The Student's tdistribution was used because 0'1 and 0'2 are unknown