In a Completely Randomized Experimental Design, 3 brands of paper towels were tested for their ability to absorb water. Equal-sized towels were used, with three sections of towels tested per brand. Excel was used to perform the ANOVA analysis of the data using alpha = 0.05. The Excel-generated output is given below:SUMMARY GroupsCountSumAverageVariance Brand X328093.3333333334.33333333 Brand Y328996.333333336.333333333 Brand Z324882.6666666742.33333333 ANOVA Source of VariationSSdfMSFP-valueF critBetween Groups309.55555562154.77777785.594377510.0425324585.14325285Within Groups166627.66666667 Total475.55555568 The null hypothesis states that there is no significant difference between the population mean absorbency ratings for these three different brands of paper towel. After looking at the Excel-generated ANOVA output above, do you believe the null? EXPLAIN YOUR ANSWER, and identify the specific part of the Excel-generated ANOVA output that supports your decision. BE SPECIFIC!!

Answered: In a Completely Randomized Experimental…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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In a Completely Randomized Experimental Design, 3 brands of paper towels were tested for their ability to absorb water. Equal-sized towels were used, with three sections of towels tested per brand. Excel was used to perform the ANOVA analysis of the data using alpha = 0.05. The Excel-generated output is given below:

SUMMARY
Groups	Count	Sum	Average	Variance
Brand X	3	280	93.33333333	34.33333333
Brand Y	3	289	96.33333333	6.333333333
Brand Z	3	248	82.66666667	42.33333333


ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	309.5555556	2	154.7777778	5.59437751	0.042532458	5.14325285
Within Groups	166	6	27.66666667

Total	475.5555556	8

The null hypothesis states that there is no significant difference between the population mean absorbency ratings for these three different brands of paper towel. After looking at the Excel-generated ANOVA output above, do you believe the null? EXPLAIN YOUR ANSWER, and identify the specific part of the Excel-generated ANOVA output that supports your decision. BE SPECIFIC!!

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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