Answered: A manufacturer is testing its new grain…

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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Question

A manufacturer is testing its new grain moisture meter and sampled out 5 grain types (1, 2, 3, 4, 5) and measured their moisture contents at 3 trials each as shown in second table. A. Compute for the estimate of the variance between treatments, compute for the degrees of freedom between treatments. B. Compute for the estimate of the variance within treatments, compute for the degrees of freedom within treatments. C. When you are asked to compute if there is a significant difference in the means at 1% level of significance, what will be the critical f value? Indicate input arguments used in looking at the table. Compute for the observed variance ratio. What will this say about the effect of grain sample to the moisture content? D. Now supposed you were asked to determine which means are different from the rest, you conduct Fisher’s least significant difference test at 10% alpha level. Find critical t value from the t-distribution table, indicate input arguments used. What is the LSD? Check if means of sample 1 is significantly different from sample 5.

Sample Replication
MC
1
7.14739
1
2
6.01415
3
8.42143
12.1292
13.0347
1
2
12.4647
1
13.9927
3
14.3569
13.5796
15.7074
16.6088
3
15.8992
1
21.0591
21.6560
3
21.3732
2.
4.

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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