Answered: sports writer wished to see if a…

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 20 adult male volunteers. These volunteers were randomly divided into two groups of 10 subjects 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 x¯1=30 yards with a standard deviation s1=9s1=9 yards. The mean yardage for group 2 was x¯2=27 yards with a standard deviation s2=6yards. Assume the two groups of kicks are independent. Let μ1 and μ2 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 and an air-filled football. Assume that two-sample t procedures are safe to use. Suppose the researcher had wished to test the hypotheses : μ1=μ2 : μ1>μ2 The numerical value of the two-sample t statistic is:

Select one:

2.57.

1.75

0.88.

1.46.

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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