Assume that each sample is obtained by randomly selecting values from a population with a normal distribution.
Off-season football players often participate in community events and charity fundraisers. Suppose a firm is bidding to provide T-shirts for players who are representing the CFL in such events. The firm has randomly sampled CFL quarterbacks and slotbacks, with these results based on data from the CFL website:
Quarterbacks: n = 10 = 192.7 lb s = 11.7 lb
Slotbacks: n = 11 = 195.0 lb s = 14.3 lb
a. Construct a 95% confidence interval estimate for the standard deviation σ for the quarterbacks.
b. Construct a 95% confidence interval estimate for the standard deviation σ for the slotbacks.
c. Assume that weight is a rough indicator of required T-shirt size, and that the firm sells a T-shirt with just enough stretchiness to fit the variation in sizes of quarterbacks. Would it be reasonable to assume that this same style of T-shirts could also fit all of the slotbacks? Explain why or why not.