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

244	262	255	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	192	215	222	216	228	207
225	208	195	191	207	196	182	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

Answer 1

(X1 – X2) + ta/2,DF) (S}/n1) + (S}/n2)

DF = ((S/n1+ s/n2))/((S/nl)/n1 - 1) + (S/n2)/n2 - 1))

Answer 2

	football ( X )	Σ ( Xi- X̅ )2	basketball ( Y )	Σ ( Yi- Y̅ )2
	246	190.44	202	13.69
	263	10.24	200	32.49
	254	33.64	220	204.49
	251	77.44	210	18.49
	244	249.64	192	187.69
	276	262.44	215	86.49
	240	392.04	221	234.09
	265	27.04	216	106.09
	257	7.84	228	497.29
	252	60.84	207	1.69
	282	492.84	225	372.49
	256	14.44	208	5.29
	250	96.04	195	114.49
	264	17.64	191	216.09
	270	104.04	207	1.69
	275	231.04	196	94.09
	245	219.04	182	561.69
	275	231.04	193	161.29
	253	46.24	201	22.09
	265	27.04
	272	148.84
Total	5455	2939.84	3909	2931.71

Mean X̅ = Σ Xi / n
X̅ = 5455 / 21 = 259.8
Sample Standard deviation S_X = √ ( (Xi - X̅ )² / n - 1 )
S_X = √ ( 2939.84 / 21 -1 ) = 12.1

Mean Y̅ = ΣYi / n
Y̅ = 3909 / 19 = 205.7
Sample Standard deviation S_Y = √ ( (Yi - Y̅ )² / n - 1 )
S_Y = √ ( 2931.71 / 19 -1) = 12.8

part a)

X1 = 259.8

S1 = 12.1

X2 = 205.7

S2 = 12.8

Part b)

Confidence interval :-

t(α/2, DF) = t(0.01 /2, 37 ) = 2.715

(X1 – X2) + ta/2,DF) (S}/n1) + (S}/n2)

DF = ((S/n1+ s/n2))/((S/nl)/n1 - 1) + (S/n2)/n2 - 1))


DF = ((12.124/21+12.7621-/19))/((12.1242/21-/21-1)+(12.7621-/19)/19-

DF = 37

(259.7619 - 205.7368) + 10.01/2.37 (12.1242/21) + (12.76212/19)

Lower Limit =
(259.7619 - 205.7368) - €0.01/2.37 (12.1242/21) + (12.76212/19)

Lower Limit = 43.3
Upper Limit =
(259.7619 - 205.7368) + +0.01/2.37 (12.1242/21) + (12.76212/19)

Upper Limit = 64.7
99% Confidence interval is ( 43.3 , 64.7 )