Independent random samples of professional football andbasketball players gave the following information. Assume that theweight distributions are mound-shaped and symmetric.

Weights (in lb) of pro football players:x₁; n₁ = 21

247	262	254	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	193	215	222	216	228	207
225	208	195	191	207	196	182	193	201

(a) Use a calculator with mean and standard deviation keys tocalculate x₁, s₁,x₂, and s₂. (Round youranswers to one decimal place.)

x1 =
s1 =
x2 =
s2 =

(b) Let μ₁ be the population mean forx₁ and let μ₂ be thepopulation mean for x₂. Find a 99% confidenceinterval for μ₁ − μ₂.(Round your answers to one decimal place.)

lower limit   Â
upper limit   Â

(c) Examine the confidence interval and explain what it means inthe context of this problem. Does the interval consist of numbersthat are all positive? all negative? of different signs? At the 99%level of confidence, do professional football players tend to havea higher population mean weight than professional basketballplayers?

Because the interval contains only negative numbers, we can saythat professional football players have a lower mean weight thanprofessional basketball players.Because the interval contains bothpositive and negative numbers, we cannot say that professionalfootball players have a higher mean weight than professionalbasketball players.    Because the intervalcontains only positive numbers, we can say that professionalfootball players have a higher mean weight than professionalbasketball players.

(d) Which distribution did you use? Why?

The standard normal distribution was used becauseσ₁ and σ₂ are unknown.

The standard normal distribution was used becauseσ₁ and σ₂ areknown.    

The Student's t-distribution was used becauseσ₁ and σ₂ are unknown.

The Student's t-distribution was used becauseσ₁ and σ₂ are known.