Group Problems - Hypothesis Testing
CIVL 3103
1. Suppose that an engineering firm is asked to check the safety of a dam. What
type of error would it commit if it erroneously rejects the null hypothesis that the
dam is safe? What type of error would it commit if it erroneously accepts the null
hypothesis that the dam is safe? What would the likely impact of these errors be?
-,
2. An experiment was performed to compare abrasive wear of two different
laminated materials. Twelve pieces of material 1 were tested by exposing each
piece to a-machine measuring wear. Ten pieces of material 2 were similarly
tested. In each case, the depth of wear was observed. The samples of material 1
gave an average wear of 85 units with a sample standard deviation of 4, while the
samples of material 2 gave an average of 81 and a sample standard deviation of 5.
Can we conclude that the abrasive wear of material 1 exceeds that of material 2
by more than 2 units? Use a p-value to determine your answer. Assume the
populations to be approximately normal with equal variances.
3. Arsenic concentration in public drinking water supplies is a potential health risk.
An article in the Arizona Republic (Sunday, May 27, 2001) reported drinking
water arsenic concentrations in parts per billion (ppb) for 10 metropolitan Phoenix
communities and 10 communities in rural Arizona. The data are shown in the
table below. Determine if there is any difference in mean arsenic concentrations
between metropolitan Phoenix communities and communities in rural Arizona at
the ex = 0.05 level of significance. Assume the populations to be approximately
normal with unequal variances.
Metro Phoenix
Phoenix, 3
Chandler, 7
Gilbert, 25
Glendale, 10
Paradise Valley, 6
Peoria, 12
Scottsdale, 25
Tempe, 15
Sun City, 7
Mesa, 15
Rural Arizona
Rimrock,48
Goodyear, 44
New River, 40
Apachie Junction, 38
Nogales, 21
Black Canyon City, 20
Sedona, 12
Payson, 1
Casa Grande, 18
Buckeye, 33
4. An article in the Journal of Strain Analysis (1983, Vol. 18, No.2) compares
several methods for predicting the shear strength for steel plate girders. Data for
two of these methods, the Karlsruhe and Lehigh procedures when applied to nine
specific girders, are shown in the table below. Determine whether the Karlsruhe
Method produces higher strength predictions on average than does the Lehigh
method, at the a = 0.0 I level of significance.
Girder
1
2
3
Karlsruhe Method
1.186
1.151
1.322
Lehigh Method
1.061
0.992
1.063
4
1.339
1.062
5
1.200
1.065
6
1.402
1.178
7
1.365
1.037
8
1.537
1.086
9
1.559
1.052
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Column 1
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Confidence Level(95.0%)
12.5
2.414079074
11
7
7.633988327
58.27777778
-0.438203372
0.767040306
22
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25
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10
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0.119
0.159
0.259
0.277
0.138
0.224
0.328
0.451
0.507
Column 1
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
0.273555556
0.045186684
0.259
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0.018376528
-0.560604493
0.687695234
0.388
0.119
0.507
2.462
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Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
27.5
4.853978895
27
#N/A
15.34962902
235.6111111
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