Question

In: Statistics and Probability

Independent random samples of professional football and basketball players gave the following information. Heights (in ft)...

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 μ1μ2. (Round your answers to three decimal places.)

lower limit    
upper limit    

Solutions

Expert Solution

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 )



Related Solutions

Independent random samples of professional football and basketball players gave the following information. Heights (in ft)...
Independent random samples of professional football and basketball players gave the following information. Heights (in ft) of pro football players: x1; n1 = 45 6.34 6.50 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 6.67 6.50 5.84 Heights (in ft) of pro basketball players: x2; n2 = 40...
Independent random samples of professional football and basketball players gave the following information. Assume that the...
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 = 21 249 263 255 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 271 Weights (in lb) of pro basketball players: x2; n2 = 19 203 200 220 210 193 215 223 216 228 207 225 208 195 191 207...
Independent random samples of professional football and basketball players gave the following information. Assume that the...
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 = 21 244 262 256 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 272 Weights (in lb) of pro basketball players: x2; n2 = 19 203 200 220 210 193 215 222 216 228 207 225 208 195 191 207...
Independent random samples of professional football and basketball players gave the following information. Assume that the...
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 = 21 249 261 256 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 271 Weights (in lb) of pro basketball players: x2; n2 = 19 202 200 220 210 191 215 223 216 228 207 225 208 195 191 207...
Independent random samples of professional football and basketball players gave the following information. Assume that the...
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 = 21 247 262 255 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 272 Weights (in lb) of pro basketball players: x2; n2 = 19 202 200 220 210 193 215 222 216 228 207 225 208 195 191 207...
Independent random samples of professional football and basketball players gave the following information. Assume that the...
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 = 21 248 262 254 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 271 Weights (in lb) of pro basketball players: x2; n2 = 19 205 200 220 210 191 215 221 216 228 207 225 208 195 191 207...
Independent random samples of professional football and basketball players gave the following information. Assume that the...
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...
Independent random samples of professional football and basketball players gave the following information. Assume that the...
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 = 21 247 262 254 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 271 Weights (in lb) of pro basketball players: x2; n2 = 19 205 200 220 210 193 215 222 216 228 207 225 208 195 191 207...
Independent random samples of professional football and basketball players gave the following information. Assume that the...
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 = 21 248 263 254 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 270 Weights (in lb) of pro basketball players: x2; n2 = 19 202 200 220 210 193 215 222 216 228 207 225 208 195 191 207...
Part 1) Independent random samples of professional football and basketball players gave the following information. Assume...
Part 1) 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 = 21 248 261 255 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 270 Weights (in lb) of pro basketball players: x2; n2 = 19 203 200 220 210 191 215 221 216 228 207 225 208 195...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT