Available below are amounts of arsenic in samples of brown rice from three different regions. The amounts are in micrograms of arsenic and all samples have the same serving size. Use a 0.05 significance level to test the claim that the three samples are from populations with the same mean. Do the amounts of arsenic appear to be different in the different regions? Given that the amounts of arsenic in the samples from region B have the highest mean, can we conclude that brown rice from region B poses the greatest health problem? Arsenic amounts (micrograms) A 1.8 3.6 4.1 4.2 4.5 4.5 4.6 4.9 5.1 5.2 5.3 5.8 B 5.6 5.7 6.7 6.9 6.9 6.9 7.1 7.2 7.4 7.5 7.7 7.8 C 4.6 4.7 5.2 5.5 5.6 5.6 5.6 5.7 6.1 6.1 6.2 6.4 What are the hypotheses to test? H0: H1: Does this support a conclusion that the brown rice from region B poses the greatest health problem? A. Since the conclusion is to fail to reject H0, do not conclude that region B poses the greatest health problem. B. Since the conclusion is to fail to reject H0 and the mean arsenic amount is greatest in region B, conclude that region B poses the greatest health problem. C. Since the conclusion is to reject H0 and the mean arsenic amount is greatest in region B, conclude that region B poses the greatest health problem. D. Since the conclusion is to reject H0, do not conclude that region B poses the greatest health problem. E. While this seems reasonable, this cannot be determined from the results of the ANOVA test.

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

Available below are amounts of arsenic in samples of brown rice from three different regions. The amounts are in micrograms of arsenic and all samples have the same serving size. Use a

0.05

significance level to test the claim that the three samples are from populations with the same mean. Do the amounts of arsenic appear to be different in the different regions? Given that the amounts of arsenic in the samples from region B have the highest mean, can we conclude that brown rice from region B poses the greatest health problem?

Arsenic amounts (micrograms)


A	1.8	3.6	4.1	4.2	4.5	4.5	4.6	4.9	5.1	5.2	5.3	5.8
B	5.6	5.7	6.7	6.9	6.9	6.9	7.1	7.2	7.4	7.5	7.7	7.8
C	4.6	4.7	5.2	5.5	5.6	5.6	5.6	5.7	6.1	6.1	6.2	6.4

What are the hypotheses to test?

H0:

H1:

Does this support a conclusion that the brown rice from region

poses the greatest health problem?

Since the conclusion is to fail to reject

H0,

do not conclude that region

poses the greatest health problem.

Since the conclusion is to fail to reject

and the mean arsenic amount is greatest in region

conclude that region

poses the greatest health problem.

Since the conclusion is to reject

and the mean arsenic amount is greatest in region

conclude that region

poses the greatest health problem.

Since the conclusion is to reject

H0,

do not conclude that region

poses the greatest health problem.

While this seems reasonable, this cannot be determined from the results of the ANOVA test.

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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