Statistics for the Behavioral Sciences
3rd Edition
ISBN: 9781506386256
Author: Gregory J. Privitera
Publisher: SAGE Publications, Inc
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Chapter 6, Problem 27PR
To determine
Explain why is it informative to know whether the data set is
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Question 2
A nickel-titanium alloy is used to make components for jet turbine aircraft engines. Cracking is a potentially
serious problem in the final part because it can lead to nonrecoverable failure. A test is run at the parts producer
to determine the effect of four factors on cracks. The four factors are: pouring temperature (A), titanium content
(B), heat treatment method (C), amount of grain refiner used (D). Two replicates of a 24 design are run, and
the length of crack (in mm x10-2) induced in a sample coupon subjected to a standard test is measured. The
data are shown in Table 2.
1
(a) Estimate the factor effects. Which factor effects appear to be large?
(b) Conduct an analysis of variance. Do any of the factors affect cracking? Use a = 0.05.
(c) Write down a regression model that can be used to predict crack length as a function of the significant
main effects and interactions you have identified in part (b).
(d) Analyze the residuals from this experiment.
(e) Is there an…
A 24-1 design has been used to investigate the effect of four factors on the resistivity of a silicon wafer. The data
from this experiment are shown in Table 4.
Table 4: Resistivity Experiment for Exercise 5
Run
A
B
с
D
Resistivity
1
23
2
3
4
5
6
7
8
9
10
11
12
I+I+I+I+Oooo
0
0
||++TI++o000
33.2
4.6
31.2
9.6
40.6
162.4
39.4
158.6
63.4
62.6
58.7
0
0
60.9
3
(a) Estimate the factor effects. Plot the effect estimates on a normal probability scale.
(b) Identify a tentative model for this process. Fit the model and test for curvature.
(c) Plot the residuals from the model in part (b) versus the predicted resistivity. Is there any indication on
this plot of model inadequacy?
(d) Construct a normal probability plot of the residuals. Is there any reason to doubt the validity of the
normality assumption?
Stem1: 1,4
Stem 2: 2,4,8
Stem3: 2,4
Stem4: 0,1,6,8
Stem5: 0,1,2,3,9
Stem 6: 2,2
What’s the Min,Q1, Med,Q3,Max?
Chapter 6 Solutions
Statistics for the Behavioral Sciences
Ch. 6.3 - Prob. 1.1LCCh. 6.3 - Prob. 1.2LCCh. 6.3 - Prob. 1.3LCCh. 6.3 - Prob. 1.4LCCh. 6.5 - Prob. 2.1LCCh. 6.5 - Prob. 2.2LCCh. 6.5 - Prob. 2.3LCCh. 6.6 - Prob. 3.1LCCh. 6.6 - Prob. 3.2LCCh. 6.6 - Prob. 3.3LC
Ch. 6.6 - Prob. 3.4LCCh. 6.7 - Prob. 4.1LCCh. 6.7 - Prob. 4.2LCCh. 6.7 - Prob. 4.3LCCh. 6.9 - Prob. 5.1LCCh. 6.9 - Prob. 5.2LCCh. 6.9 - Prob. 5.3LCCh. 6.10 - Prob. 6.1LCCh. 6.10 - Prob. 6.2LCCh. 6 - Prob. 1FPCh. 6 - Prob. 2FPCh. 6 - Prob. 3FPCh. 6 - Prob. 4FPCh. 6 - Prob. 5FPCh. 6 - Prob. 6FPCh. 6 - Prob. 7FPCh. 6 - Prob. 8FPCh. 6 - Prob. 9FPCh. 6 - Prob. 10FPCh. 6 - Prob. 11CAPCh. 6 - Prob. 12CAPCh. 6 - Prob. 13CAPCh. 6 - Prob. 14CAPCh. 6 - Prob. 15CAPCh. 6 - Prob. 16CAPCh. 6 - Prob. 17CAPCh. 6 - Prob. 18CAPCh. 6 - Prob. 19CAPCh. 6 - Prob. 20CAPCh. 6 - Prob. 21CAPCh. 6 - Prob. 22CAPCh. 6 - Prob. 23CAPCh. 6 - Prob. 24CAPCh. 6 - Prob. 25CAPCh. 6 - Prob. 26PRCh. 6 - Prob. 27PRCh. 6 - Prob. 28PRCh. 6 - Prob. 29PRCh. 6 - Prob. 30PRCh. 6 - Prob. 31PRCh. 6 - Prob. 32PR
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- A clinical study is designed to assess the average length of hospital stay of patients who underwent surgery. A preliminary study of a random sample of 70 surgery patients’ records showed that the standard deviation of the lengths of stay of all surgery patients is 7.5 days. How large should a sample to estimate the desired mean to within 1 day at 95% confidence? Round your answer to the whole number.arrow_forwardIn the experiment a sample of subjects is drawn of people who have an elbow surgery. Each of the people included in the sample was interviewed about their health status and measurements were taken before and after surgery. Are the measurements before and after the operation independent or dependent samples?arrow_forwardiid 1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution depend on the mean and variance of the underlying random variables (i.e., the population mean and variance). The approximation can be written to emphasize this, using the expec- tation and variance of one of the random variables in the sample instead of the parameters μ, 02: YNEY, · (1 (EY,, varyi n For the following population distributions f, write the approximate distribution of the sample mean. (a) Exponential with rate ẞ: f(y) = ß exp{−ßy} 1 (b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ } г( (c) Poisson with rate λ: P(Y = y) = exp(-\} > y! y²arrow_forward
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