King Fahd University of Petroleum & Minerals
Department of Mathematics & Statistics
STAT-319-Term081-Quiz5A-SOLUTIONS
Name:
ID:
Sec.:
Serial: _____
1. Consider nonconforming bricks from a brick manufacturing process. Typically, 5% of the bricks
produced are not suitable for construction purposes. The production engineer monitors this process by
periodically collecting random samples and classifying the bricks as conforming or nonconforming. A
recent sample of 250 bricks yielded 20 nonconforming. Construct a 98% confidence interval for the
true proportion of nonconforming bricks.
98% C.I  0.98 = 1 -   =0.02. So, /2 = 0.01. (1pt)
p  x / n = 20/250 = 0.08 (1pt)
98% CI for p:
p  Z /2
p(1  p)
n
. (1pt)
0.08(1  0.08)
 0.08  2.33
250
= 0.08 + 2.33(0.017158)
(1pt)
= 0.08 + 0.039978
=(0.040022, 0.119978)
Interpret: We are 98% confident that the true proportion of nonconforming bricks is between
0.040022 and 0.119978
(1pt)
2. The brightness (in microamps) of a television picture tube can be evaluated by measuring the amount of
current required to achieve a particular brightness level. A random sample of 10 tubes results in a
mean X =317.2 and a standard deviation s = 15.7. Find a 99% confidence interval on the mean current
required.
n =10 x =?. population x = unknown and small samples. So use t with df = n-1 = 10-1 = 9 (1pt)
99% C.I  0.99 = 1 -   =0.01.
So, /2 = 0.005.  t/2 .= t0.005 = 3.25 from t table (column = 0.05, row =df=9) (1pt)
99% CI for :
s
x  t /2
n
. (1pt)
15.7
 317.2  3.25
10
= 317.2 + 3.25(4.964781)
= 317.2 + 16.1355
=(301.0645, 333.3355)
Interpret: We are 99% confident that the true mean of required current is between 301.0645 and
333.3355.
(1pt)
State any necessary assumptions you must make to obtain the above confidence interval.
X must be from a normal population
(1pt)
= 10 + 5 (4) =30
King Fahd University of Petroleum & Minerals
Department of Mathematics & Statistics
STAT-319-Term081-Quiz5B-SOLUTIONS
Name:
ID:
Sec.:
Serial: _____
1. Consider nonconforming bricks from a brick manufacturing process. Typically, 5% of the bricks
produced are not suitable for construction purposes. The production engineer monitors this process by
periodically collecting random samples and classifying the bricks as conforming or nonconforming. A
recent sample of 300 bricks yielded 24 nonconforming. Construct a 96% confidence interval for the
true proportion of nonconforming bricks.
96% C.I  0.96 = 1 -   =0.04. So, /2 = 0.02. (1pt)
p  x / n = 24/300 = 0.08 (1pt)
96% CI for p:
p  Z /2
p(1  p)
n
.
(1pt)
0.08(1  0.08)
300
= 0.08 + 2.05(0.015663)
(1pt)
= 0.08 + 0.032109
=(0.047891, 0.112109)
Interpret: We are 96% confident that the true proportion of nonconforming bricks is between
0.047891 and 0.112109
(1pt)
 0.08  2.05
2. The brightness (in microamps) of a television picture tube can be evaluated by measuring the amount of
current required to achieve a particular brightness level. A random sample of 10 tubes results in a
mean X =327.2 and a standard deviation s = 15.7. Find a 95% confidence interval on the mean current
required.
n =10 x =?. population x = unknown and small samples. So use t with df = n-1 = 10-1 = 9 (1pt)
99% C.I  0.99 = 1 -   =0.01.
So, /2 = 0.005.  t/2 .= t0.005 = 3.25 from t table (column = 0.05, row =df=9) (1pt)
99% CI for :
s
x  t /2
n
. (1pt)
15.7
 327.2  3.25
10
= 327.2 + 3.25(4.964781)
= 327.2 + 16.1355
=(311.0645, 343.3355)
Interpret: We are 99% confident that the true mean of required current is between 311.0645 and
343.3355.
(1pt)
State any necessary assumptions you must make to obtain the above confidence interval.
X must be from a normal population
(1pt)
/12 + 8/12 = 6 - 4 = 2
King Fahd University of Petroleum & Minerals
Department of Mathematics & Statistics
STAT-319-Term081-Quiz5C-SOLUTIONS
Name:
ID:
Sec.:
Serial: _____
1. Consider nonconforming bricks from a brick manufacturing process. Typically, 5% of the bricks
produced are not suitable for construction purposes. The production engineer monitors this process by
periodically collecting random samples and classifying the bricks as conforming or nonconforming. A
recent sample of 300 bricks yielded 24 nonconforming. Construct a 97% confidence interval for the
true proportion of nonconforming bricks.
96% C.I  0.96 = 1 -   =0.04. So, /2 = 0.02. (1pt)
p  x / n = 24/300 = 0.08 (1pt)
96% CI for p:
p  Z /2
p(1  p)
n
.
(1pt)
0.08(1  0.08)
300
= 0.08 + 2.05(0.015663)
(1pt)
= 0.08 + 0.032109
=(0.047891, 0.112109)
Interpret: We are 96% confident that the true proportion of nonconforming bricks is between
0.047891 and 0.112109
(1pt)
 0.08  2.05
2. The brightness (in microamps) of a television picture tube can be evaluated by measuring the amount of
current required to achieve a particular brightness level. A random sample of 10 tubes results in a
mean X =327.2 and a standard deviation s = 15.7. Find a 90% confidence interval on the mean current
required.
n =10 x =?. population x = unknown and small samples. So use t with df = n-1 = 10-1 = 9 (1pt)
99% C.I  0.99 = 1 -   =0.01.
So, /2 = 0.005.  t/2 .= t0.005 = 3.25 from t table (column = 0.05, row =df=9) (1pt)
99% CI for :
s
x  t /2
n
. (1pt)
15.7
 327.2  3.25
10
= 327.2 + 3.25(4.964781)
= 327.2 + 16.1355
=(311.0645, 343.3355)
Interpret: We are 99% confident that the true mean of required current is between 311.0645 and
343.3355.
(1pt)
State any necessary assumptions you must make to obtain the above confidence interval.
X must be from a normal population
(1pt)
/12 + 8/12 = 6 - 4 = 2