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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 33PPS
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Question
  1. 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.  
  1. 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) 
  1. Determine the p-value in (a) and interpret its meaning. 
  1. In addition to equal variances, what other assumption is necessary in (a)? 
  1. 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
Transcribed Image Text: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
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