Pro Football and Basketball: Heights 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). Note: These data are also available for download at the Companion Sites for this text.

Heights (in ft) of pro football players: x1; n1 5 45 6.33 6.50 6.50 6.25 6.50 6.33 6.25 6.17 6.42 6.33 6.42 6.58 6.08 6.58 6.50 6.42 6.25 6.67 5.91 6.00 5.83 6.00 5.83 5.08 6.75 5.83 6.17 5.75 6.00 5.75 6.50 5.83 5.91 5.67 6.00 6.08 6.17 6.58 6.50 6.25 6.33 5.25 6.67 6.50 5.83 Heights (in ft) of pro basketball players: x2; n2 5 40 6.08 6.58 6.25 6.58 6.25 5.92 7.00 6.41 6.75 6.25 6.00 6.92 6.83 6.58 6.41 6.67 6.67 5.75 6.25 6.25 6.50 6.00 6.92 6.25 6.42 6.58 6.58 6.08 6.75 6.50 6.83 6.08 6.92 6.00 6.33 6.50 6.58 6.83 6.50 6.58

(a) Use a calculator with mean and standard deviation keys to verify that x1 < 6.179, s1 < 0.366, x2 < 6.453, and s2 < 0.314.

(b) Let m1 be the population mean for x1 and let m2 be the population mean for x2. Find a 90% confidence interval for m1 2m2.

(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 90% level of confidence, do professional football players tend to have a higher population mean height than professional basketball players?

(d) Check Requirements Which distribution

(standard normal or Student’s t) did you use?

Why? Do you need information about the height distributions? Explain.

AppendixLO1