Answered: than a football filled with air. To…

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

A sports writer wished to see if a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 18 adult male volunteers. These volunteers were randomly divided into two groups of nine men each. Group 1 kicked a football that was filled with helium to the recommended pressure. Group 2 kicked a football that was filled with air to the recommended pressure. The mean yardage for Group 1 was ?¯1=300 yards with a standard deviation of ?1=8 yards. The mean yardage for Group 2 was ?¯2=296 yards with a standard deviation of ?2=6 yards. Assume the two groups of kicks are independent. Let ?1 and ?2 represent the mean yardage we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium‑filled football and an air‑filled football.

Assuming two‑sample ? procedures are safe to use and using Option 1 for the degrees of freedom, a 90% confidence interval for ?1−?2 is:

(−1.848,9.8477) .

(−1.82,9.8196) .

(−3.112,11.112)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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