In: Statistics and Probability
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 |
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 SX = √ ( (Xi - X̅
)2 / n - 1 )
SX = √ ( 5.8793 / 45 -1 ) = 0.366
Mean Y̅ = ΣYi / n
Y̅ = 258.14 / 40 = 6.454
Sample Standard deviation SY = √ ( (Yi - Y̅
)2 / n - 1 )
SY = √ ( 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 )