Question #4In a test of weight loss programs, 192 subjects were divided such that 32 subjects followed each of 6 diets. Each was weighed a year after starting the diet and the results are in the ANOVA table below. Use a 0.05significance level to test the claim that the mean weight loss is the same for the different diets.Source of VariationSSdfMSFP-valueF critBetween Groups459.438591.887552.81850.0176842.262672Within Groups6063.89418632.60158 Total6523.332191 Should the null hypothesis that all the diets have the same mean weight loss be rejected? A. Yes, because the P-value is less than the significance level.B. No, because the P-value is less than the significance level.C. No, because the P-value is greater than the significance level.D. Yes, because the P-value is greater than the significance level.

Answered: Should the null hypothesis that all the…

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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Question #4

In a test of weight loss programs, 192 subjects were divided such that 32 subjects followed each of 6 diets. Each was weighed a year after starting the diet and the results are in the ANOVA table below. Use a 0.05significance level to test the claim that the mean weight loss is the same for the different diets.

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	459.438	5	91.88755	2.8185	0.017684	2.262672
Within Groups	6063.894	186	32.60158
Total	6523.332	191

Should the null hypothesis that all the diets have the same mean weight loss be rejected?

A. Yes, because the P-value is less than the significance level.

B. No, because the P-value is less than the significance level.

C. No, because the P-value is greater than the significance level.

D. Yes, because the P-value is greater than the significance 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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