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

248 261 256 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 271

Weights (in lb) of pro basketball players:x₂;n₂= 19

205 200 220 210 191 215 222 216 228 207 225 208 195 191 207 196 183 193 201

(a) Use a calculator with mean and standard deviation keys to calculatex₁,s₁,x₂, ands₂. (Round your answers to one decimal place.)x₁=s₁=x₂=s₂=

(b) Let₁be the population mean forx₁and let₂be the population mean forx₂. Find a 99% confidence interval for₁₂.(Round your answers to one decimal place.)lower limitupper limit

(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.

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.

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?

The standard normal distribution was used because₁and₂are known.

The standard normal distribution was used because₁and₂are unknown.

The Student'st-distribution was used because₁and₂are known.

The Student'st-distribution was used because₁and₂are unknown.