Sporting goods manufacturing company wanted to compare the distance travelled by golf balls produced using each of 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 balls 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 travelled in yards) for the four designs were as follows. Distance Travelled 1 2 3 4 206.32 217.08 226.77 230.55 207.94 221.43 224.79 227.95 206.19 218.04 229.75 231.84 204.45 224.13 228.51 224.87 209.65 211.82 221.44 229.49 203.81 213.9 223.85 231.1 206.75 221.28 223.97 221.53 205.68 229.43 234.3 235.45 204.49 213.54 219.5 228.35 210.86 214.51 233.0 225.09 A one-way ANOVA of the above data is given as follows: Source of Variation SS df MS F P-value F crit Between Groups (i) (ii) (v) (vii) 2.73E-13 2.866266 Within Groups 676.8244 (iii) (vi) Total 3667.814 (iv) Fill the missing values (i) to (vii). At the 0.05 level of significance, is there evidence of a difference in the mean distances travelled by the golf balls with different designs? If the results in (1) indicate that it is appropriate, use a one-way ANOVA procedure to determine which designs differ in mean distances.

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Description: Sporting goods manufacturing company wanted to compare the distance travelled by golf balls produced using each of four different designs. Ten balls were manufactured with each design and were brought to the local golf course for the club professiona

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Sporting goods manufacturing company wanted to compare the distance travelled by golf balls produced using each of 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 balls 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 travelled in yards) for the four designs were as follows.

Distance Travelled	1	2	3	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	213.9	223.85	231.1
	206.75	221.28	223.97	221.53
	205.68	229.43	234.3	235.45
	204.49	213.54	219.5	228.35
	210.86	214.51	233.0	225.09

A one-way ANOVA of the above data is given as follows:

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	(i)	(ii)	(v)	(vii)	2.73E-13	2.866266
Within Groups	676.8244	(iii)	(vi)

Total	3667.814	(iv)

Fill the missing values (i) to (vii).
At the 0.05 level of significance, is there evidence of a difference in the mean distances travelled by the golf balls with different designs?
If the results in (1) indicate that it is appropriate, use a one-way ANOVA procedure to determine which designs differ in mean distances.
What assumptions are necessary in (1)?
What golf ball design should the manufacturing manager choose? Explain

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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