What can we say about comparing the weights of professional football players to

Question

What can we say about comparing the weights of professional football players to the weights of professional basketball players? A random sample of 27 professional football players gave a sample mean weight x = 257.5 pounds. A random sample of 17 professional basketball players gave a sample mean weight of y = 238.8 pounds. It is recognized that the standard deviation of football player weights is sigma_x = 23 pounds while it is recognized that the standard deviation of basketball player weights is sigma_y = 20 pounds. The true (unknown) true mean for football player weights is mu_x pounds while the true (unknown) mean for basketball player weights is mu_y pounds. a) Calculate the variance of the random variable X which is the mean of 27 football player weights b) Calculate the variance of the random variable Y, which is the mean of 17 basketball player weights. c) Calculate the variance of X - Y? d) Calculate the standard deviation of X - Y? e) If we wish to create a 92% confidence interval for mu_x - mu_y then what is the z critical value used? f) Create a 92% confidence interval for mu_x - mu_y. () g) What is the length of your 92% confidence interval for mu_x - mu_y ? h) If we used this data to test H_0: mu_x - mu_y = 0 against the alternative H_a: mu_x - mu_y

Explanation / Answer

a) Variance of random variable X will be = 23^2 = 529

b) Variance of random variable X will be = 20^2 = 400

c) Variance of X-Y = 529-400 = 129

d) Standard deviation of X-Y = sqrt(129) = 11.358

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