Answered: Vanadium has recently been recognized…

Name: Vanadium has recently been recognized as an important trace element. A
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Description: Vanadium has recently been recognized as an important trace element. An experiment was conducted to compare the concentrations of vanadium in different foods. The amount of vanadium, measured in nanograms per gram, was recorded for 8 samples of each

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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Vanadium has recently been recognized as an important trace element. An experiment was conducted to compare the concentrations of vanadium in different foods. The amount of vanadium, measured in nanograms per gram, was recorded for 8 samples of each of the following foods: green beans, tuna, and soy milk. The output from an ANOVA is shown below:

State the null and alternative hypotheses to carry out ANOVA with these data.

a) H₀: Food products and level of vanadium are related
H_a: Food products and vanadium are not related

b) H₀: Food products and level of vanadium are not related
H_a: Food products and level of vanadium are related

c) H₀: There is a difference in the mean level of vanadium among the three food products
H_a: There is no difference in the mean level of vanadium among the three food products

d) H₀: There is no difference in the mean level of vanadium among the three food products
H_a: There is a difference in the mean level of vanadium among the three food products

One-way ANOVA: Green Beans, Tuna, Soy Milk
Analysis of variance
Source DF
MS F-Value P-value
Factor
2
3.118
1.559
2.88
0.078
Error
21
11.371
0.541
Total
23
14.489

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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