Pro Football and Basketball: Weights of Players Independent random samples of pr

Question

Pro Football and Basketball: Weights of Players Independent random samples of professional football and basketball players gave the following information (References: Sports Encyclopedia of Pro Football and Official NBA Basketball Encyclopedia). These data are also available for download at the Online Study Center. Assume that the weight distributions are mound shaped and symmetric. Weights (in lb) of pro football players: X_1, n_i = 21 245 262 255 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 270 Weights (in lb) of pro basketball players: x_2; n_2 = 19 205 200 220 210 191 215 221 216 228 207 225 208 195 191 207 196 181 193 201 (a) Use a calculator with mean and standard deviation keys to verify that x_i almostequalto 259.6, x_1 almostequalto 12.1, x_2 almostequalto 205.8, and s_2 almostequalto 12.9. (b) Let mu_1 be the population mean for x_1 and let be the population mean for x_2. Find a 99% confidence interval for mu_1 - mu_2. (c) Interpretation Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, do professional football players tend to have a higher population mean weight than professional basketball players? (d) Which distribution (standard normal or Student's t) did you use? Why?

Explanation / Answer

a)do it on calculator

b)Observed difference (Sample 1 - Sample 2): 53.8

Equal Variances
Pooled Standard Deviation: = sqrt((s1^2 + s2^2)/2) = 12.4853
Pooled DF: n1 + n2 - 2 = 38

t0.005=2.712

hence 99% Confidence Interval for the Difference

(53.8 - 2.712*12.4853 *sqrt(1/21+1/19),(53.8 + 2.712*12.4853 *sqrt(1/21+1/19))

(43.07907,64.52092)

c) interval contains all positive numbers.

since each data in confidence interval is positive ,the given hypothesis is true .

d)we used t-distribution, as population variance were unknown.

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