Answered: Four fabrics are tested for…

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

Four fabrics are tested for flammability at the National Bureau of Standards. Burn times (in seconds) are recorded after a paper tab is ignited on the hem of a dress made of each fabric. ## Load the data from our course website (HW06_FabricData.csv) into a data frame named *FabricData*. The burn times will be contained in the *BurnTime* variable of the data frame (FabricData\$BurnTime) and the conditions (i.e. fabric number) will be contained in the *Fabric* variable (FabricData\$Fabric).

If F is significant, use RStudio to perform a Tukey test of all pairs of means in the study. Compute your values step-by-step (i.e. do not use the *TukeyHSD()* function) with $\alpha$ = .05. Report HSD, all pairwise mean differences, and interpret the results.

Perform a Scheffe test, comparing Fabric 4 to Fabrics 2 and 3 combined using rstudio.

Perform a Scheffe test, comparing Fabric 1 to Fabrics 2, 3, and 4 combined.

BurnTime Fabric
17.8 Fab1
16.2 Fab1
17.5 Fab1
17.4 Fab1
15 Fab1
11.2 Fab2
11.4 Fab2
15.8 Fab2
10 Fab2
10.4 Fab2
11.8 Fab3
11 Fab3
10
Fab3
9.2 Fab3
9.2 Fab3
14.9 | Fab4
10.8 | Fab4
12.8 | Fab4
10.7 | Fab4
10.7 | Fab4

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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