A sporting goods manufacturing company wanted to compare the distance traveled by golf balls produced using four different designs. Nine 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 was randomized to the pro did not know which type of ball was being hit. All 36 balls were hit (assuming the environmental conditions played no role). The resulting distances in yards were recorded and are shown in the following table: Design 1Design 2Design 3Design 4206.32217.08226.77230.55207.94221.43224.79227.95206.19218.04229.75231.84204.45224.13228.51224.87209.65211.82221.44229.49203.81213.90223.85231.10206.75221.28223.97221.53205.68229.43234.30235.45204.49213.54219.50228.35 Write a set of hypotheses to test the mean difference in distances of the four golf ball designs. Ho: Ha: Draw a diagram or picture to depict the rejection region and the test being utilized, label the rejection region and critical value(s).Is there evidence of a difference in the mean distances traveled by the various golf ball designs (test at α = 0.05).

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. Nine 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 was randomized to the pro did not know which type of ball was being hit. All 36 balls were hit (assuming the environmental conditions played no role). The resulting distances in yards were recorded and are shown in the following table:

*Design 1*	*Design 2*	*Design 3*	*Design 4*
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

Write a set of hypotheses to test the mean difference in distances of the four golf ball designs.

H_o:

H_a:

Draw a diagram or picture to depict the rejection region and the test being utilized, label the rejection region and critical value(s).
Is there evidence of a difference in the mean distances traveled by the various golf ball designs (test at α = 0.05).

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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