Studies have shown that exposure to light at night is harmful to human health. A study in mice shows that light at night has an effect on weight gain after just three weeks. In the study, mice were randomly assigned to live in one of three light conditions: LD had a standard light/dark cycle, LL had bright light all the time, and DM had dim light when there normally would have been darkness. Activity Levels Perhaps the mice with light at night gain more weight because they are exercising less. The conditions for an ANOVA test are met and computer output is shown for testing the average activity level for each of the three light conditions. The null hypothesis is that mean activity level is not related to light condition, while the alternative hypothesis is that the mean activity level is related to light condition. Is there a significant difference in mean activity level? Level N Mean StDev DM 10 2503 1999 LD 8 2433 2266 LL 9 2862 2418 One-way ANOVA: Activity versus Light Source DF SS MS F P Light 2 935954 467977 0.09 0.910 Error 24 118718447 4946602 Total 26 119654401 What is the F-statistic? What is the p-value? What is the conclusion of the test? Is there a significant difference in mean activity level?

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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LIGHT AT NIGHT MAKES FAT MICE

Studies have shown that exposure to light at night is harmful to human health. A study in mice shows that light at night has an effect on weight gain after just three weeks. In the study, mice were randomly assigned to live in one of three light conditions: LD had a standard light/dark cycle, LL had bright light all the time, and DM had dim light when there normally would have been darkness.

Activity Levels

Perhaps the mice with light at night gain more weight because they are exercising less. The conditions for an ANOVA test are met and computer output is shown for testing the average activity level for each of the three light conditions. The null hypothesis is that mean activity level is not related to light condition, while the alternative hypothesis is that the mean activity level is related to light condition. Is there a significant difference in mean activity level?

Level	N	Mean	StDev
DM	10	2503	1999
LD	8	2433	2266
LL	9	2862	2418

One-way ANOVA: Activity versus Light

Source	DF	SS	MS	F	P
Light	2	935954	467977	0.09	0.910
Error	24	118718447	4946602
Total	26	119654401

What is the F-statistic?

What is the p-value?

What is the conclusion of the test?

Is there a significant difference in mean activity level?

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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