One of the factors that determines the degree of risk a pesticide poses to human health is the rate at which the pesticide is absorbed into skin after contact. An important question is whether the amount in the skin continues to increase with the length of the contact, or whether it increases for only a short time before leveling off. To investigate this, measured amounts of a certain pesticide were applied to 20 samples of rat skin. Four skins were analyzed at each of the time intervals 1, 2, 4, 10, and 24 hours. The amounts of the chemical (in micrograms) that were in the skin are given in the following table. Duration Amounts Absorbed1 1.31.41.32.12 1.62.01.32.04 1.91.62.11.710 2.02.12.01.724 2.42.22.62.2Can you conclude that the amount in the skin varies with time? Use the =α0.001 level of significance and the ANOVA table shown below.One-way ANOVA: Pesticide AmountSourceDFSSMSFPDuration41.51500.378754.970.009Error151.1430.07617 Total192.657 Is there enough evidence to conclude that the mean amount of pesticide in the skin varies with time?

Name: One of the factors that determines the degree of risk a pesticide pose
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Description: One of the factors that determines the degree of risk a pesticide poses to human health is the rate at which the pesticide is absorbed into skin after contact. An important question is whether the amount in the skin continues to increase with the len

Given: The provided ANOVA table is: One-way ANOVA: Pesticide Amount Source DF SS MS F…

Answered: One of the factors that determines the…

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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One of the factors that determines the degree of risk a pesticide poses to human health is the rate at which the pesticide is absorbed into skin after contact. An important question is whether the amount in the skin continues to increase with the length of the contact, or whether it increases for only a short time before leveling off. To investigate this, measured amounts of a certain pesticide were applied to

samples of rat skin. Four skins were analyzed at each of the time intervals

, and

hours. The amounts of the chemical (in micrograms) that were in the skin are given in the following table.

Duration	Amounts Absorbed
1	1.3	1.4	1.3	2.1
2	1.6	2.0	1.3	2.0
4	1.9	1.6	2.1	1.7
10	2.0	2.1	2.0	1.7
24	2.4	2.2	2.6	2.2

Can you conclude that the amount in the skin varies with time? Use the

=α0.001

level of significance and the ANOVA table shown below.

One-way ANOVA: Pesticide Amount
Source	DF	SS	MS	F	P
Duration	4	1.5150	0.37875	4.97	0.009
Error	15	1.143	0.07617
Total	19	2.657

Is there enough evidence to conclude that the mean amount of pesticide in the skin varies with time?

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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