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The Islamic University of Gaza
Faculty of Engineering
Department of Civil Engineering
9/1/2010
Statistics and Probability for Engineering Applications
ENGC 6310 - Dr. Samir Safi
Practice Problems for Chapter 13 & 14
Solution
1- A die is tossed 180 times with the following results:
x 1 2 3 4 5 6
f 28 36 36 30 27 23
Is this a balanced die? Use a 0.01 level of significance.
2- In 100 tosses of a coin, 63 heads and 37 tails are observed. Is this a balanced
coin? Use a 0.05 level of significance.
1
3- A random sample of 90 adults is classified according to gender and the
number of hours they watch television during a week:
Watching
Gender
Television
Male Female
Over 25 hours
15
29
Under 25
27
19
hours
Use a 0.01 level of significance and test the hypothesis that the time spent
watching television is independent of whether the viewer is male or female.
4- The following responses concerning the standard of living at the time of an
independent opinion poll of 1000 households versus one year earlier seems to
be in agreement with the results of a study published in Across the Board (June
1981):
Period
Standard of Living
Somewhat Better Same Good
1980: Jan.
72
144
84
May
63
135
102
Sep.
47
100
53
1981: Jan.
40
105
55
Test the hypothesis that the proportions of households within each standard of
living category are the same for each of the four time periods. Use a P-value.
2
5- The grades of a class of 9 students on a midterm report (x) and on the final
examination (y) are as follows:
x 77 50 71 72 81 94 96 99 67
y 82 66 78 34 47 85 99 99 68
(a) Estimate the linear regression line.
(b) Estimate the final examination grade of a student who received a grade of
85 on the midterm report.
3
6- In a certain type of metal test specimen, the normal stress on a specimen is
known to be functionally related to the shear resistance. The following is a set
of coded experimental data on the two variables:
Normal Stress, X Shear Resistance, Y
26.8
26.5
25.4
27.3
28.9
24.2
23.6
27.1
27.7
23.6
23.9
25.9
24.7
26.3
28.1
22.5
26.9
21.7
27.4
21.4
22.6
25.8
25.6
24.9
(a) Estimate the regression line
(b) Estimate the shear resistance for a normal stress of 24.5 kilograms per
square centimeter.
4