9. [-/4.42 Points] DETAILS BBUNDERSTAT12 7.4.014.S. Independent random samples of professional football and basketball p

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9 4 42 Points Details Bbunderstat12 7 4 014 S Independent Random Samples Of Professional Football And Basketball P 1 (162.8 KiB) Viewed 14 times

9. [-/4.42 Points] DETAILS BBUNDERSTAT12 7.4.014.S. 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 = 21 244 261 256 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 272 (a) Use a calculator with mean and standard deviation keys to calculate X₁, S₁, X2, and s₂. (Round your answers to four decimal places.) X1 $1 x2 = Weights (in lb) of pro basketball players: x2; n2 = 19 205 200 220 210 192 215 221 216 228 207 225 208 195 191 207 196 181 193 201 $2= USE SALT (b) Let μ₁ be the population mean for X₁ and let μ2 be the population mean for X₂. Find a 99% confidence interval for μ₁ −μ₂. (Round your answers to one decimal place.) lower limit upper limit MY NOTES (d) Which distribution did you use? Why? o The standard normal distribution was used because 01 and 02 are unknown. O The Student's t-distribution was used because 01 and °2 are unknown. o The standard normal distribution was used because ₁ and 2 are known. o The Student's t-distribution was used because ₁ and 2 are known. ASK YOUR TEACHER (c) 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? Because the interval contains only negative numbers, we can say that professional football players have a lower mean weight than professional basketball players. O 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. O Because the interval contains only positive numbers, we can say that professional football players have a higher mean weight than professional basketball players.