Mathematical Statistics with Applications
7th Edition
ISBN: 9781133384380
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
Publisher: Cengage Learning US
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Textbook Question
Chapter 14.5, Problem 23E
The χ2 test used in Exercise 14.22 is equivalent to the two-tailed Z test of Section 10.3, provided α is the same for the two tests. Show algebraically that the χ2 test statistic X2 is the square of the test statistic Z for the equivalent test.
14.22 A study to determine the effectiveness of a drug (serum) for the treatment of arthritis resulted in the comparison of two groups each consisting of 200 arthritic patients. One group was inoculated with the serum whereas the other received a placebo (an inoculation that appears to contain serum but actually is not active). After a period of time, each person in the study was asked whether his or her arthritic condition had improved. The results in the accompanying table were observed. Do these data present sufficient evidence to indicate that the proportions of arthritic individuals who said their condition had improved differed depending on whether they received the serum?
- a Test by using the X2 statistic. Use α = .05.
- b Test by using the Z test of Section 10.3 and α = .05. Compare your result with that in part (a).
- c Give bounds for the attained significance level associated with the test in part (a).
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Question 4
An article in Quality Progress (May 2011, pp. 42-48) describes the use of factorial experiments to improve a
silver powder production process. This product is used in conductive pastes to manufacture a wide variety of
products ranging from silicon wafers to elastic membrane switches. Powder density (g/cm²) and surface area
(cm/g) are the two critical characteristics of this product. The experiments involved three factors: reaction
temperature, ammonium percentage, stirring rate. Each of these factors had two levels, and the design was
replicated twice. The design is shown in Table 3.
A222222222222233
Stir Rate
(RPM)
Ammonium
(%)
Table 3: Silver Powder Experiment from Exercise 13.23
Temperature
(°C)
Density
Surface Area
100
8
14.68
0.40
100
8
15.18
0.43
30
100
8
15.12
0.42
30
100
17.48
0.41
150
7.54
0.69
150
8
6.66
0.67
30
150
8
12.46
0.52
30
150
8
12.62
0.36
100
40
10.95
0.58
100
40
17.68
0.43
30
100
40
12.65
0.57
30
100
40
15.96
0.54
150
40
8.03
0.68
150
40
8.84
0.75
30
150…
Chapter 14 Solutions
Mathematical Statistics with Applications
Ch. 14.3 - Historically, the proportions of all Caucasians in...Ch. 14.3 - Prob. 2ECh. 14.3 - Prob. 3ECh. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10E
Ch. 14.3 - The data in the following table are the frequency...Ch. 14.4 - On the 40th anniversary of President John F....Ch. 14.4 - A study was conducted by Joseph Jacobson and Diane...Ch. 14.4 - Suppose that the entries in a contingency table...Ch. 14.4 - A survey to explore the relationship between...Ch. 14.4 - Prob. 17ECh. 14.4 - Prob. 18ECh. 14.4 - The results of a study suggest that the initial...Ch. 14.4 - Refer to Exercise 14.10. Test the hypothesis, at...Ch. 14.4 - An interesting and practical use of the 2 test...Ch. 14.5 - A study to determine the effectiveness of a drug...Ch. 14.5 - The 2 test used in Exercise 14.22 is equivalent to...Ch. 14.5 - How do Americans in the sandwich generation...Ch. 14.5 - Does education really make a difference in how...Ch. 14.5 - A manufacturer of buttons wished to determine...Ch. 14.5 - Traditionally, U.S. labor unions have been content...Ch. 14.5 - Prob. 29ECh. 14.5 - Refer to Exercise 14.29. Estimate the difference...Ch. 14.5 - A survey was conducted to investigate interest of...Ch. 14 - Prob. 32SECh. 14 - A survey was conducted to determine student,...Ch. 14 - How would you rate yourself as a driver? According...Ch. 14 - Prob. 35SECh. 14 - Knee injuries are a major problem for athletes in...Ch. 14 - It is often not clear whether all properties of a...Ch. 14 - Prob. 39SECh. 14 - Prob. 40SECh. 14 - Prob. 41SECh. 14 - Prob. 42SECh. 14 - Prob. 43SE
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