Penicillin is produced by the Penicillium fungus, which is grown in a broth whose sugar content must be carefully controlled. Several samples of broth were taken on three successive days, and the amount of dissolved sugars, in milligrams per milliliter, was measured on each sample. The results were as follows.Day 1:5.25.55.14.95.35.05.25.15.45.24.85.15.4 Day 2:5.85.15.35.55.24.95.45.05.45.05.65.45.6 Day 3:5.94.95.25.35.15.45.35.85.55.45.45.45.2 Can you conclude that the mean sugar concentration differs among the three days? Use the =α0.05 level of significance and the ANOVA table shown below.One-way ANOVA: Sugar ConcentrationSourceDFSSMSFPDays20.28510.14262.31350.1134Error362.21850.0616 Total382.5036 Yes or no, we, can or can not, conclude that the mean sugar concentration differs among the three days.

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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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Penicillin is produced by the Penicillium fungus, which is grown in a broth whose sugar content must be carefully controlled. Several samples of broth were taken on three successive days, and the amount of dissolved sugars, in milligrams per milliliter, was measured on each sample. The results were as follows.

Day 1 :	5.2	5.5	5.1	4.9	5.3	5.0	5.2
5.1	5.4	5.2	4.8	5.1	5.4
Day 2 :	5.8	5.1	5.3	5.5	5.2	4.9	5.4
5.0	5.4	5.0	5.6	5.4	5.6
Day 3 :	5.9	4.9	5.2	5.3	5.1	5.4	5.3
5.8	5.5	5.4	5.4	5.4	5.2

Can you conclude that the mean sugar concentration differs among the three days? Use the

=α0.05

level of significance and the ANOVA table shown below.

Source	DF	SS	MS	F	P
One-way ANOVA: Sugar Concentration
Days	2	0.2851	0.1426	2.3135	0.1134
Error	36	2.2185	0.0616
Total	38	2.5036

Yes or no, we, can or can not, conclude that the mean sugar concentration differs among the three days.

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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