Answered: Your friend suggests that the mean…

Name: Your friend suggests that the mean number of errors for outfielders is
Uploaded: 2024-03-20T07:06:16.000Z
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Description: Your friend suggests that the mean number of errors for outfielders is the same regardless of the position played. You question this so you take the following random sample of 15 outfielders, who played the same number of games, and record the number

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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Your friend suggests that the mean number of errors for outfielders is the same regardless of the position played. You question this so you take the following random sample of 15 outfielders, who played the same number of games, and record the number of errors they made the previous season.

Left Field Center Field Right Field

10 12 9

8 10 8

7 9 7

6 13 8

8 11 9

Show the important statistics and interpret all results. Ensure the ANOVA table is presented along with your discussion.
Provide anything else that is helpful.

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 + ...

Expert Solution

Step 1

The hypothesis is,

$H_{0} : T h e m e a n o f a l l f i e l d i s s a m e . V S H_{1} : A t l e a s t o n e m e a n i s d i f f e r e n t .$

Step 2

The Excel output of ANOVA is,

SUMMARY
Groups	Count	Sum	Average	Variance
left field	5	39	7.8	2.2
center field	5	55	11	2.5
Right field	5	41	8.2	0.7


ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	30.4	2	15.2	8.444444	0.005137	3.885294
Within Groups	21.6	12	1.8

Total	52	14

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