Answered: Independent random samples of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Independent random samples of professional football and basketball players gave the following information. Assume that the weight distributions are mound-shaped and symmetric.

Weights (in lb) of pro football players: x₁; n₁ = 21

243	261	254	251	244	276	240	265	257	252	282
256	250	264	270	275	245	275	253	265	271

Weights (in lb) of pro basketball players: x₂; n₂ = 19

204	200	220	210	193	215	222	216	228	207
225	208	195	191	207	196	183	193	201

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to four decimal places.)

x₁ =
s₁ =
x₂ =
s₂ =

(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.)

lower limit
upper limit

(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 Student's t-distribution was used because ?₁ and ?₂ are unknown. The Student's t-distribution was used because ?₁ and ?₂ are known.The standard normal distribution was used because ?₁ and ?₂ are known.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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