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 Companion Sites for this text.

Heights (in ft) of pro football players: x₁; n₁ = 45

Heights (in ft) of pro basketball players: x₂; n₂ = 40

(a) Use a calculator with mean and standard deviation keys to verify that x̅₁ » 6.179, s₁ » 0.366, x̅₂ » 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 – m².

(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.

Transcribed Image Text:

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 6.67 591 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 6.0 6.17 6.58 6.50 6.25 6.33 5.25 6.67 6.50 5.83 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