Answered: A company manufactures tennis balls.…

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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A company manufactures tennis balls. When its tennis balls are dropped onto a concrete surface from a height of

100

inches, the company wants the mean height the balls bounce upward to be

54.9

inches. This average is maintained by periodically testing random samples of

tennis balls. If the t-value falls between

−t0.95

and

t0.95,

then the company will be satisfied that it is manufacturing acceptable tennis balls. A sample of

balls is randomly selected and tested. The mean bounce height of the sample is

56.1

inches and the standard deviation is

0.25

inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls?

Find −t0.95 and t0.95.

Find T- value

Is the company making acceptable tennies balls

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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