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STAT 211
SPRING 2003
FINAL EXAM - FORM A

Write your name and student id on the exam.

You have 75 minutes to complete this exam. There are 25 questions (100 pts. total) and there is no partial
credit on this exam.

Make sure to mark your name, student id and the test form on the scantron. Also, sign your scantron.

If numeric numbers (such as MINITAB outputs or any other type of information) are given for different
questions, do not try to compute them again. Just use the given information. Otherwise, you will be reducing
the time you have.

You can only use your own calculator and 3-pages of formulas. Sharing the formulas or calculator with others
is considered as cheating. There is penalty of 5 pt. if you separate your exam with any reason.

If you did not mark your final answer on your scantron, your answer will be counted incorrect.

If you did not mark your exam form on the scantron , the lowest grade of two forms will be assigned by the
computer and your grade will not be corrected later.

You should not have the same color for the exam with the person next to you. If you caught cheating, you will
get a grade of zero. Good Luck.
Consider the following case and answer questions 1 to 3 using this case.
Decision
Population
H
Ha
0
Garment
manufacturing
Clothing expenditure
 = $200 (on target)
H 0 if
Reject
  $200 (off target)
Decision
Fail to reject
Garment
manufacturing
$195  x  $205
x  $195 (Revise plan for lower
(Use present plan)
expenditures) or
_
H 0 if
_
_
x  $205 (Revise plan for higher
expenditures)
_
1.
I believe that clothing expenditure is off target. I collected the data and saw that the sample mean is x  200 .
I made my decision on this sample data. Which of the following may be the possible error based on this
decision?
a. Type I error
b. Type II error
c. Correct decision
2.
Which of the following is the probability of type II error if  = $199, =$20 and n=100 in normally distributed
population?
a. 0.1972
b. 0.4207
c. 0.6179
d. 0.9759
e. 0.9987
3.
Which of the following is the decision and the conclusion for the garment manufacturing?
_
a.
H 0 is rejected if x  210 and present plan is used
b.
H 0 is not rejected if x  210 and present plan is used
c.
H 0 is rejected if x  210 and revised plan is used
d.
H 0 is not rejected if x  210 and revised plan is used
e.
none of the above
_
_
_
X and Y are the continuous random variables with the joint pdf,
kxy2 ,
f ( x, y)  
0,
0  x 1
0 y2
otherwise
Answer the next 3 questions using this information. Notice that you can still answer questions 5 and 6 without
knowing the numeric value of k.
4.
Which of the following k makes f(x,y) a legitimate joint pdf?
a. any positive number
b. 1/4
c. 1/3
d. 3/4
e. 4/3
5.
Which of the following is the marginal pdf of y?
2
a.
f(y)= ky
/ 2 , 0<y<2
b. f(y)= 8ky / 3, 0<y<2
c.
f(y)= 8ky
2
/ 3, 0<y<2
f(y)= 3ky
2
/ 8, 0<y<2
d.
6.
If f ( x)  8kx / 3, 0<x<1, which of the following is E(X)?
a. 8k/9
b. 4k/3,
c. 2k/3
d. k/9
Let X1,…,Xm be a random sample from normal distribution with the mean
1
and the variance
 12 .
Let Y1,…,Yn
be a random sample from normal distribution with the mean  2 and the variance  . The data are as follows:
1
2
3
4
5
6
7
8
sample mean
sample variance
X
-3
-2
-1
0
1
2
3
0
0.8165
Y
-4
-3
-2
-1
1
2
3
4
0
1.0351
2
2
Answer the next 4 questions using the information above.
7.
Which of the following is the median of X?
a. -2
b. -1
c. 0
d. 1
e. 2
8.
Which of the following has the higher variability?
a. X
b. Y
c. Both X and Y
d. Neither X nor Y
9.
Which of the following is the maximum likelihood estimator for
a. -2
b. -1
c. 0
d. 1
e. 2


_
_
21 - 3 2 ?


10. Which of the following is the point estimate of Var  2 x  3 y  ?
a.
b.
c.
d.
e.
0.4666
0.6979
1.6311
6.2783
12.5819
11. I am interested in observing if the true number of damaged helmets children using in rural areas are more than
the number of damaged helmets children using in urban areas. Which of the following hypothesis should be
used to test this?
a. Lower tailed test
b. Upper tailed test
c. Two tailed test
The amount of radon released in showers was investigated. Radon-enriched water was used in the experiment, and
six different orifice diameters were tested in showerheads. The data from the experiment are shown in the following
table.
Orifice Diameter Radon Released (%)
0.37
80 83 83 85
0.51
75 75 79 79 78 76
0.71
74 73 76 77
1.02
67 72 74 74
1.40
62 62 67 69
1.99
58 61 61 61 60 62 59 61
We are interested in observing if the size of the orifice affect the mean percentage of radon released. We will use
the notation 1 ,  2 ,  3 ,  4 ,  5 ,  6 for the true mean percentage of radon released for the sizes 0.37, 0.51, 0.71,
1.02, 1.40. 1.99, respectively. The true means being the same implies the size of the orifice does not affect the
percentage of radon released. The data are found to be normally distributed. The following are the results of single
factor ANOVA, Tukey’s pairwise comparisons, equal variance testing obtained by MINITAB.
Analysis of Variance for radon
Source
DF
SS
MS
diam
5
1760.23
352.05
Error
23
125.21
5.44
Total
28
1885.45
Level
0.37
0.51
0.71
1.02
1.40
1.99
N
4
6
4
4
4
8
Mean
82.750
77.000
75.000
71.750
65.000
60.429
F
64.67
StDev
2.062
1.897
1.826
3.304
3.559
1.512
95% Tukey's pairwise comparisons for
0.37
P
0.000
0.51
i   j :
0.71
1.02
0.51
1.075
10.425
0.71
2.628
12.872
-2.675
6.675
1.02
5.878
16.122
0.575
9.925
-1.872
8.372
1.40
12.628
22.872
7.325
16.675
4.878
15.122
1.628
11.872
1.99
17.782
26.861
12.542
20.601
10.032
19.111
6.782
15.861
1.40
0.032
9.111
(those two numbers for each combination (i,j) are the confidence interval limits on Tukey’s intervals)
Bartlett's Test (normal distribution)
Test Statistic: 4.385
P-Value
: 0.495
Use the information and the MINITAB outputs above to answer the following 6 questions.
Use =0.05 when it is necessary.
12. What percent of radon released data is higher than 59% for the size 1.99?
a. 0.25
b. 0.375
c. 0.50
d. 0.675
e. 0.75
13. If I ask you to tell me the degrees of freedom to compute 95% confidence interval for
1   6
as we discussed
in Chapter 9, what would you tell me?
a. I have to know if the population variances are the same. There is no information given
b. I have to know the population variances to calculate it.
c. 6
d. 8
e. 10
14. Which of the following is the point estimate for
a.
b.
c.
d.
e.
3  5 ?
-10
-5.75
0
5.75
10
15. Which of the following would be the test statistics if I asked you to test the sizes 0.37 and 1.02 having the same
true variance?
a. 0.3895
b. 0.6241
c. 0.7899
d. 0.9357
16. Which of the following would be the test statistics if I asked you to test the true standard deviation for the size
1.99 being 2.2? (Hint: You are finding the test statistics for H 0 :  6  2.2 where  6 is the true standard
deviation for the size 1.99)
a. 1.4170
b. 3.3064
c. 6.3513
d. 14.8197
17. I computed the 95% confidence interval for the true variance of the size 0.37 as (1.3645, 59.0534). If I claim
that the true standard deviation of the size 0.37 is 8, is my claim rejected based on the given information?
a. Yes. The claimed true variance of the size 0.37 falls in 95% confidence interval for the true variance.
b. No. The claimed true variance of the size 0.37 falls in 95% confidence interval for the true variance.
c. Yes. The claimed true variance of the size 0.37 does not fall in 95% confidence interval for the true
variance.
d. No. The claimed true variance of the size 0.37 does not fall in 95% confidence interval for the true
variance.
18. In which of the following cases, you would use t as your test statistics?
a. Only when the sample size is small in any normally distributed population
b. Only when the sample size is large in any normally distributed population
c. When the sample size is small and population standard deviation is unknown in normally distributed
population
d. When the sample size is large and population standard deviation is unknown in normally distributed
population
19. The distance between major cracks in a highway follows an exponential distribution with a mean of 10 miles.
What is the standard deviation of the distance between major cracks?
a. 0.01
b. 0.1
c. 10
d. 100
20. If the test statistics is computed as z=-1.3 in a lower tailed test, which of the following would be the
corresponding P-value?
a. 0.0968
b. 0.1936
c. 0.8064
d. 0.9032
21. If the test statistics is computed as z=-0.92 in a two-tailed test, which of the following would be the
corresponding P-value?
a. 0.1788
b. 0.3576
c. 0.6424
d. 0.8212
22. If the 95% two-sided confidence interval for the true proportion of students against the tuition increase is
computed as (0.6652, 0.8349), which of the following would be the possible conclusion based on this?
a. 70% of students against the tuition increase
b. More than 70% of students against the tuition increase
c. At most 70% of students against the tuition increase
23. If we decrease the confidence level for the confidence interval of the true mean keeping everything else being
the same, which of the following is correct?
a. The confidence interval becomes larger
b. The width of the confidence interval becomes smaller
c. The true standard deviation does change
d. Sample size does change
_
24. What is the confidence level for the interval
a.
b.
c.
d.
e.
x  1.01 
?
15
I do not have the table attached to my exam to answer this question
0.3752
0.5314
0.6876
0.8438
25. If the P-value is 0.13 and =0.05, would you reject
a.
b.
c.

H0 ?
I need to know if this is upper tailed, lower tailed or two tailed test
Yes
No
Answer Key:
1.b
2.d
14.e
15.a
3.c
16.b
4.d
17.c
5.a
18.c
6.a
19.c
7.c
20.a
8.b
21.b
9.c
22.a
10.c
23.b
11.b
24.d
12.e
25.c
13.e