Question

Independent random samples of professional football and basketball players gave the following information.

Heights (in ft) of pro football players: x₁; n₁ = 45

6.33	6.52	6.50	6.25	6.50	6.33	6.25	6.17	6.42	6.33
6.42	6.58	6.08	6.58	6.50	6.42	6.25	6.67	5.91	6.00
5.83	6.00	5.83	5.08	6.75	5.83	6.17	5.75	6.00	5.75
6.50	5.83	5.91	5.67	6.00	6.08	6.17	6.58	6.50	6.25
6.33	5.25	6.66	6.50	5.82

Heights (in ft) of pro basketball players: x₂; n₂ = 40

6.08	6.56	6.25	6.58	6.25	5.92	7.00	6.41	6.75	6.25
6.00	6.92	6.85	6.58	6.41	6.67	6.67	5.75	6.25	6.25
6.50	6.00	6.92	6.25	6.42	6.58	6.58	6.08	6.75	6.50
6.83	6.08	6.92	6.00	6.33	6.50	6.58	6.83	6.50	6.58

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to three decimal places.)

x1 =
s1 =
x2 =
s2 =

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find a 90% confidence interval for μ₁ – μ₂. (Round your answers to three decimal places.)

lower limit
upper limit

Answer 1

	football ( X )	Σ ( Xi- X̅ )2	basketball ( Y )	Σ ( Yi- Y̅ )2
	6.33	0.0228	6.08	0.1394
	6.52	0.1163	6.56	0.0114
	6.5	0.1031	6.25	0.0413
	6.25	0.0051	6.58	0.0161
	6.5	0.1031	6.25	0.0413
	6.33	0.0228	5.92	0.2844
	6.25	0.0051	7	0.2989
	6.17	0.0001	6.41	0.0019
	6.42	0.0581	6.75	0.088
	6.33	0.0228	6.25	0.0413
	6.42	0.0581	6	0.2055
	6.58	0.1609	6.92	0.2178
	6.08	0.0098	6.85	0.1574
	6.58	0.1609	6.58	0.0161
	6.5	0.1031	6.41	0.0019
	6.42	0.0581	6.67	0.05
	6.25	0.0051	6.67	0.047
	6.67	0.2412	5.75	0.4946
	5.91	0.0723	6.25	0.0413
	6	0.032	6.25	0.0413
	5.83	0.1217	6.5	0.0022
	6	0.032	6	0.2055
	5.83	0.1217	6.92	0.2178
	5.08	1.2076	6.25	0.0413
	6.75	0.3262	6.42	0.0011
	5.83	0.1217	6.58	0.0161
	6.17	0.0001	6.58	0.0161
	5.75	0.184	6.08	0.1394
	6	0.032	6.75	0.088
	5.75	0.184	6.5	0.0022
	6.5	0.1031	6.83	0.1419
	5.83	0.1217	6.08	0.1394
	5.91	0.0723	6.92	0.2178
	5.67	0.259	6	0.2055
	6	0.032	6.33	0.0152
	6.08	0.0098	6.5	0.0022
	6.17	0.0001	6.58	0.0161
	6.58	0.1609	6.83	0.1419
	6.5	0.1031	6.5	0.0022
	6.25	0.0051	6.58	0.0161
	6.33	0.0228
	5.25	0.8629
	6.66	0.2315
	6.5	0.1031
	5.82	0.1288
Total	278.05	5.908	258.13	3.8619

part a)

Mean X̅ = Σ Xi / n
X̅ = 278.05 / 45 = 6.179
Sample Standard deviation S_X = √ ( (Xi - X̅ )² / n - 1 )
S_X = √ ( 5.9074 / 45 -1 ) = 0.366

Mean Y̅ = ΣYi / n
Y̅ = 258.13 / 40 = 6.453
Sample Standard deviation S_Y = √ ( (Yi - Y̅ )² / n - 1 )
S_Y = √ ( 3.8609 / 40 -1) = 0.315

X1 = 6.179

S1 = 0.366

X2 = 6.453

S2 = 0.315

Confidence interval :-

t(α/2, DF) = t(0.1 /2, 82 ) = 1.664

DF = 82

Lower Limit =
Lower Limit = -0.397
Upper Limit =
Upper Limit = -0.151
90% Confidence interval is ( -0.397 , -0.151 )