Answered: A sporting goods manufacturing company…

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 sporting goods manufacturing company wanted to compare the distance traveled by golf

balls produced using four different designs. Ten balls were manufactured with each design and

were brought to the local golf course for the club professional to test. The order in which the

balls were hit with the same club from the first tee was randomized so that the pro did not know

which type of ball was being hit. All 40 balls were hit in a short period of time, during which the

environmental conditions were essentially the same. The results (distance in yards) for the four

designs are stored in the table below.

a) At the 0.05 level of significance, is there evidence of a difference in the mean distances

traveled by the golf balls with different designs?

Design1	Design2	Design3	Design4
206.32	217.08	226.77	230.55
207.94	221.43	224.79	227.95
206.19	218.04	229.75	231.84
204.45	224.13	228.51	224.87
209.65	211.82	221.44	229.49
203.81	213.90	223.85	231.10
206.75	221.28	223.97	221.53
205.68	229.43	234.30	235.45
204.49	213.54	219.50	228.35
210.86	214.51	233.00	225.09

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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