Independent random samples of professional football and basketball players gave the following information. Assume that the weight distributions are mound-shaped and symmetric.
(a) Calculate the means and standard deviations: x
1,
s1, x
2, and
s2. (Round your answers to one decimal place.)
(b) Let ?
1 be the population mean for
x1 and let ?
2 be the population mean for
x2. Find a 99% confidence interval for ?
1 − ?
2. (Round your answers to one decimal place.)
(c) 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?
Because the interval contains only negative numbers, we can say that professional football players have a lower mean weight than professional basketball players.Because the interval contains both positive and negative numbers, we cannot say that professional football players have a higher mean weight than professional basketball players. Because the interval contains only positive numbers, we can say that professional football players have a higher mean weight than professional basketball players.
(d) Which distribution did you use? Why?
The standard normal distribution was used because ?1 and ?2 are unknown.The standard normal distribution was used because ?1 and ?2 are known. The Student'st-distribution was used because ?1 and ?2 are known.The Student'st-distribution was used because ?1 and ?2 are unknown.