Question

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

245	261	255	251	244	276	240	265	257	252	282
256	250	264	270	275	245	275	253	265	272

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

203	200	220	210	192	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 calculate x₁, s₁, x₂, and s₂. (Round your answers to one decimal place.)

x1 =
s1 =
x2 =
s2 =

(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

(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 Student's t-distribution was used because σ₁ and σ₂ are known.The standard normal distribution was used because σ₁ and σ₂ are unknown.     The Student's t-distribution was used because σ₁ and σ₂ are unknown.The standard normal distribution was used because σ₁ and σ₂ are known.

Answer 1

(a) From the given sample data :

(b)

The 99% confidence interval for μ₁ − μ_{2 ,}

;

lower limit=43.7

upper limit=63.9

(c) Hypothesis : Vs

Here , the value does not lies in the confidence interval

Therefore , reject the null hypothesis.

Hence , At the 99% level of confidence, the  professional football players tend to have a higher population mean weight than professional basketball players.

Because the interval contains only positive numbers

(d) The standard normal distribution was used because σ₁ and σ₂ are unknown.

Therefore , use the estimates of and