Question

Independent random samples of professional football and basketball players gave the following Information. Assume that the weight distributions are Welghts (In Ib) of pro football players: xq; n = 21 244 262 256 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 271 Weights (in lb) of pro basketball players: Xy; n2 = 19 203 200 220 210 192 215 221 216 228 207 225 208 195 191 207 196 183 193 201 (a) Use a calculator with mean and standard deviation keys to calculate X3, 5, 2, and 57. (Round your answers to one decimal place.) X- S: X2 - S2 - (b) Let yli be the population mean for Xy and let Hy be the population mean for xy. Find a 99% confidence interval for - M. (Round you lower limit upper limit

Answer 1

X 244 262 256 251 244 276 240 265 257 252 X - mean -15.6667 2.3333 -3.6667 -8.6667 -15.6667 16.3333 - 19.6667 5.3333 -2.6667 -7.6667 22.3333 -3.6667 -9.6667 4.3333 10.3333 15.3333 -14.6667 15.3333 -6.6667 5.3333 11.3333 (X-mean) 2 245.446 5.4443 13.4447 75.1117 245.446 266.777 386.779 28.4441 7.1113 58.7783 498.776 13.4447 93.4451 18.7775 106.777 235.11 215.112 235.11 44.4449 28.4441 128.444 264 270 275 245 275 253 265

Since we know that

Mean() = Li=1;

Where n is the number of data points
Now

Στη = 5453.0 i=1

and n = 21
This implies that

5453.0 Mean() = Mean() = 259.6667

Since we know that

Variance(s?) = ? n -1 xi - 5)2 = 2950.6669 n = 21 2950.6669 Variance(s) = 20 Variance(s?) = 147.5333 Standard Deviation(s) = V Variance Standard Deviation(s) = 12.1463

X 203 200 220 210 192 215 221 216 228 207 225 208 X - mean (X-mean2 -2.8421 8.0775 -5.8421 34.1301 14.1579 200.446 4.1579 17.2881 -13.8421 191.604 9.1579 83.8671 15.1579 229.762 10.1579 103.183 22.1579 490.973 1.1579 1.3407 19.1579 367.025 2.1579 4.6565 -10.8421 117.551 -14.8421 220.288 1.1579 1.3407 -9.8421 96.8669 -22.8421 521.761 -12.8421 164.919 -4.8421 23.4459 207 196 183 193 201


Στη = 3911.0 1-1

and n = 19
This implies that

3911.0 Mean(a)= 19 Mean() = 205.8421


ri - 7) = 2878.5257 n = 19 2878.5257 Variance(s) = ? 18 Variance(s?) = 159.9181 Standard Deviation(s) = V Variance Standard Deviation(s) = 12.6459

Mean1 ($\small \bar{X_1}$) = 259.6667
Standard deviation1 (s1) = 12.1463
Mean2 ($\small \bar{X_2}$) = 205.8421
Standard deviation2 (s2) = 12.6459
b) Sample size1 (n1) = 21
Sample size2 (n2) = 19
Confidence interval(in %) = 99

ta/2,1, +n2-2 = 2.7115

Since we know that

1 1 Confidence interval = X1 - X2 Eta/2.n-1 SpV +- ni 'n2 sp_./(n1 - 1)s12 + (n2 - 1)s22 V ni+n2 - 2 Required confidence interval = (259.6669–205.8421-2.7115SpV +6259.6669– 205.8421 + 2.71155pV +)

Required confidence interval = (53.8248-10.6988, 53.8248+10.6988)
Required confidence interval = (43.126, 64.5236)

lower limit = 43.126

upper limit = 64.5236
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