Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 9.1, Problem 13E
A mechanical engineer wishes to compare strength properties of steel beams with similar beams made with a particular alloy. The same number of beams, n, of each type will be tested. Each beam will be set in a horizontal position with a support on each end, a force of 2500 lb will be applied at the center, and the deflection will be measured. From past experience with such beams, the engineer is willing to assume that the true standard deviation of deflection for both types of beam is .05 in. Because the alloy is more expensive, the engineer wishes to test at level .01 whether it has smaller average deflection than the steel beam. What value of n is appropriate if the desired type II error probability is .05 when the difference in true average deflection favors the alloy by .04 in.?
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Students have asked these similar questions
Acrylic bone cement is commonly used in total joint replacement to secure the artificial joint. Data on the force (measured
in Newtons, N) required to break a cement bond was determined under two different temperature conditions and in two
different mediums appear in the following table.
Temperature Medium
Data on Breaking Force
22 degrees
Dry
100.5, 142.6, 194.8, 118.4, 176.1, 213.1
37 degrees
22 degrees
Dry
Wet
303.3, 339.1, 288.8, 306.8, 305.2, 327.5
385.4, 367.2, 322.6, 307.4, 357.9, 321.4
37 degrees
Wet
363.6, 376.8, 327.7, 331.9, 338.1, 394.6
(a) Estimate the difference between the mean breaking force in a dry medium at 37 degrees and the mean
breaking force at the same temperature in a wet medium using a 90% confidence interval. (Round your answers to
one decimal place.)
×
X )
Two types of force sensors (A and B) to measure the applied force (Ib) at the tip of a cantilever
in a student Lab. The two data sets are shown below:
1.
Standard
N
Deviation
Average
A
140.2
10.01
12
B
145.5
8.96
14
a. Estimate the interval of the true mean with 95% confidence, using data from sensor A.
b. How many more measurements are needed for sensor A to have the same interval with 99%
confidence (assume the mean and standard deviation are the same)?
c. How many measurements (out of 12) using sensor A to have force greater 142 (randomly sampled)?
d. What is the probability to have the true mean force greater 142 using sensor A?
e. Determine if there is a difference between the two sensors A and B with 95% of confidence.
A new type of fabric is claimed to be wrinkle-free. There are other wrinkle-free fabrics
in the market, but how can these be compared? Comparison is done by measuring
the wrinkle recovery angle (WRA) of the fabric, in degrees. Higher is better. The
current top brand in the market claims that their fabrics have a WRA of 141 degrees
on the average. A sample of fabrics from the new type were subjected to tests in
order to measure their WRA and the following observations were obtained:
137
141
144
144
137
135
146
138
141
139
146
139
140
140
142
Test the hypothesis that the population mean of the WRAs of the new type of fabric
exceeds that of the current top brand. Use a = 0.05.
1. Test Stat:
2. Critical Region:
a. T 1.761
c. T> abs (2.145)
d. T> 2.14
3. Conclusion: At 5% level of significance
a. the new type of fabric does not exceed the WRA of the top current brand
b. the new type of fabric exceeds the WRA of the top current brand
Chapter 9 Solutions
Probability and Statistics for Engineering and the Sciences
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