Question

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

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

6.31	6.51	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	6.65	6.50	5.83

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

6.08	6.57	6.25	6.58	6.25	5.92	7.00	6.41	6.75	6.25
6.00	6.92	6.83	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	6.85	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

	Values ( X )	Σ ( Xi- X̅ )2	Values ( Y )	Σ ( Yi- Y̅ )2
	6.31	0.0174	6.08	0.1399
	6.51	0.1102	6.57	0.0135
	6.5	0.1037	6.25	0.0416
	6.25	0.0052	6.58	0.0159
	6.5	0.1037	6.25	0.0416
	6.33	0.0231	5.92	0.2852
	6.25	0.0052	7	0.2981
	6.17	0.0001	6.41	0.0019
	6.42	0.0586	6.75	0.0876
	6.33	0.0231	6.25	0.0416
	6.42	0.0586	6	0.2061
	6.58	0.1616	6.92	0.2172
	6.1	0.0096	6.83	0.1414
	6.58	0.1616	6.58	0.0159
	6.5	0.1037	6.41	0.0019
	6.42	0.0586	6.67	0.05
	6.25	0.0052	6.67	0.0467
	6.67	0.2421	5.75	0.4956
	5.91	0.0718	6.25	0.0416
	6	0.0317	6.25	0.0416
	5.83	0.1211	6.5	0.0021
	6	0.0317	6	0.2061
	5.83	0.1211	6.92	0.2172
	5.08	1.2056	6.25	0.0416
	6.75	0.3272	6.42	0.0012
	5.83	0.1211	6.58	0.0159
	6.17	0.0001	6.58	0.0159
	5.75	0.1832	6.08	0.1399
	6	0.0317	6.75	0.0876
	5.75	0.1832	6.5	0.0021
	6.5	0.1037	6.83	0.1414
	5.83	0.1211	6.08	0.1399
	5.91	0.0718	6.92	0.2172
	5.67	0.2581	6	0.2061
	6	0.0317	6.33	0.0154
	6.08	0.0096	6.5	0.0021
	6.17	0.0001	6.58	0.0159
	6.58	0.1616	6.85	0.1568
	6.5	0.1037	6.5	0.0021
	6.25	0.0052	6.58	0.0159
	6.33	0.0231	258.14	3.864
	5.25	0.8612
	6.65	0.2228
	6.5	0.1037
	5.83	0.1211
Total	278.02	5.8793	258.14	3.864

Part a)

Mean X̅ = Σ Xi / n
X̅ = 278.02 / 45 = 6.178
Sample Standard deviation S_X = √ ( (Xi - X̅ )² / n - 1 )
S_X = √ ( 5.8793 / 45 -1 ) = 0.366

Mean Y̅ = ΣYi / n
Y̅ = 258.14 / 40 = 6.454
Sample Standard deviation S_Y = √ ( (Yi - Y̅ )² / n - 1 )
S_Y = √ ( 3.864 / 40 -1) = 0.315

x1 = 6.178

s1 = 0.366

x2 = 6.454

s2 = 0.315

Part b)

Confidence interval :-

t(α/2, DF) = t(0.1 /2, 82 ) = 1.664

DF = 82

Lower Limit =
Lower Limit = -0.399
Upper Limit =
Upper Limit = -0.153
90% Confidence interval is ( -0.399 , -0.153 )