In intaglio printing, a design or figure is carved beneath the surface of hard metal or stone. Suppose that an experiment is designed to compare differences in mean surface hardness of steel plates used in intaglio printing (measured in indentation numbers), based on two different surface conditions-untreated and treated by lightly polishing with emery paper. In the experiment, 40 steel plates are randomly assigned-20 that are untreated, and 20 that are treated. The results of the experiment are in the “Intaglio” data in Chapter 10_HW_Data.xls. Assuming that the population variances from both conditions are equal, is there evidence of a difference in the mean surface hardness between untreated and treated steel plates? (use α = 0.05) Determine the p-value in (a) and interpret its meaning. In addition to equal variances, what other assumption is necessary in (a)? Repeat Problem (a), assuming that the population variances from untreated and treated steel plates are not equal, compare the results with those of (a). AObsUntreated Treated1164.368 158.2392159.018 138.2163153.871 168.00645678165.096149.654157.184 145.456154.496 168.178160.920 154.321164.917 162.7639169.091 161.02010175.276 167,70611177.135 150.22612163.903 155.62013167.802 151.23314160.818158.65315167.433 151.20416163.538 150.86917164.525 161.65718171.230 157.01619174.964 156.67020166.311 147.920

(1) To test whether there is a significant difference in mean surface hardness between untreated and…

Answered: A Obs Untreated Treated 1 164.368…

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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In intaglio printing, a design or figure is carved beneath the surface of hard metal or stone. Suppose that an experiment is designed to compare differences in mean surface hardness of steel plates used in intaglio printing (measured in indentation numbers), based on two different surface conditions-untreated and treated by lightly polishing with emery paper. In the experiment, 40 steel plates are randomly assigned-20 that are untreated, and 20 that are treated. The results of the experiment are in the “Intaglio” data in Chapter 10_HW_Data.xls.

Assuming that the population variances from both conditions are equal, is there evidence of a difference in the mean surface hardness between untreated and treated steel plates? (use α = 0.05)

Determine the p-value in (a) and interpret its meaning.

In addition to equal variances, what other assumption is necessary in (a)?

Repeat Problem (a), assuming that the population variances from untreated and treated steel plates are not equal, compare the results with those of (a).

A
Obs
Untreated Treated
1
164.368 158.239
2
159.018 138.216
3
153.871 168.006
45678
165.096
149.654
157.184 145.456
154.496 168.178
160.920 154.321
164.917 162.763
9
169.091 161.020
10
175.276 167,706
11
177.135 150.226
12
163.903 155.620
13
167.802 151.233
14
160.818
158.653
15
167.433 151.204
16
163.538 150.869
17
164.525 161.657
18
171.230 157.016
19
174.964 156.670
20
166.311 147.920

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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