Download Exam 3 - TAMU Stat

STAT 211-200
EXAM 3- FORM A
SUMMER03
The U.S. Census Bureau produces estimates of total resident population for each state on an annual basis.
The table of the random sampled data was demonstrated for your first exam. The following is the
descriptive statistics obtained by using MINITAB software.
Variable
X:Births
Y:Deaths
U:total migration
Variable
X:Births
Y:Deaths
U:total migration
n
51
51
51
Minimum
6035
3142
-24436
Mean
79366
47958
28418
Median
54318
34066
9430
Maximum
529610
234012
299015
TrMean
64220
41493
17383
Q1
18942
12831
1507
StDev
93998
48872
59526
SE Mean
13162
6843
8335
Q3
85356
57544
34153
Answer the following 7 questions using this information.
1.
Which of the following is the point estimate for the expected value of X-Y?
(a) 20252
(b) 31408
(c) 47958
(d) 79366
2.
Which of the following is the point estimate for the standard error of X-Y?
(a) 377.9815
(b) 105943.84
(c) 142870
(d) 1.1224x1010
(e) 2.0412x1010
3.
Which of the following is the point estimate for the expected value of
(a) 20252
(b) 31408
(c) 47958
(d) 79366
4.
If X’s are normally distributed, which of the following is the MLE for the variance?
(a) 93998
(b) 173238244
(c) 8662376475
(d) 8835624004
5.
If Y’s are Poisson distributed, which of the following is the MME for the parameter ?
(a) 0.0000126
(b) 0.000020852
(c) 28418
(d) 47958
(e) 79366
6.
If U’s are normally distributed, which of the following is the point estimate for P(U < 27000)?
(a) 0.02
(b) 0.492
(c) 0.5
(d) 0.508
(e) 0.98
7.
If U’s are normally distributed, would the MLE for the variance of U be different than the point
estimate for the variance of U?
(a) Yes
(b) No
_
_
X Y ?
STAT 211-200
EXAM 3- FORM A
SUMMER03
A plastic casing for a magnetic disk is composed of two halves. The thickness of each half is normally
distributed with a mean of 1.5 millimeters and a standard deviation of 0.1 millimeter and the halves are
independent random samples. Answer the following 5 questions using this information.
8.
Which of the following is the expected value of the total thickness of the two halves?
(a) 0.75
(b) 1.5
(c) 2.25
(d) 3
9.
Which of the following is the standard error of the total thickness of the two halves?
(a) 0.02
(b) 0.14
(c) 0.22
(d) 0.42
(e) 0.60
10. What is the probability that total thickness exceeds 3.3 millimeters?
(a) 0.017
(b) 0.300
(c) 0.521
(d) 0.700
(e) 0.983
11. If halves are not independent random samples but the covariance between them is 0.2, which of the
following is the variance of the total thickness of the two halves?
(a) 0.02
(b) 0.14
(c) 0.22
(d) 0.42
(e) 0.60
12. What is the probability that thickness of one of the halves exceeds 1.5 millimeters?
(a) 0
(b) 0.25
(c) 0.5
(d) 0.75
(e) 1
^
13. Suppose that 2  1 ,
^
^
 2 /5 and  3
/4 are the unbiased estimators of the parameter
.
We know that
 ^
 ^ 
 ^ 
^
 ^ 
 ^
E  2 1   E  2 / 5   E  3 / 4    , Var  1   10 , Var 2   12 and Var 3   16 .






 
 
 
Which of the following is the minimum variance unbiased estimator for
^
(a)
 2 /5
(b)
3
^
/4
^
(c)
1 / 2
^
(d) 2  1
^
(e)
5 2
?
STAT 211-200
EXAM 3- FORM A
SUMMER03
X and Y are the continuous random variables with the joint pdf,
 x  y,
f ( x, y )  
0,
0  x 1
0  y 1
otherwise
The marginal pdf of X is calculated as
 x  0.5,
f ( x)  
0,
E(XY)=1/3
0  x 1
otherwise
E(Y)=7/12
Answer the following 3 questions using this information.
14. Which of the following is the marginal pdf for Y?
(a) f(y)=y+0.5,
0<y<1
(b) f(y)=y-0.5,
0<y<1
(c) f(y)=y+1,
0<y<1
(d) f(y)=y-1,
0<y<1
15. Is X and Y are independent?
(a) Yes
(b) No
16. Which of the following is the covariance between X and Y?
(a) -0.5833
(b) -0.3333
(c) -0.0069
(d) 0.0069
(e) 0.5833
The heat evolved in calories per gram of a cement mixture is approximately normally distributed with the
unknown mean  (true average calories per gram of a cement mixture) and the standard deviation =2. We
collected the sample of 10 specimens and computed the sample average calories per gram of a cement
mixture as 99. Answer the following 3 questions using this information.
_
17. Which of the following is the standard error for the sample average calories per gram (
(a) 0.20
(b) 0.40
(c) 0.63
(d) 1.27
(e) 2
X )?
18. Which of the following is the 95% confidence interval for ?
(a) (97.76 , 100.24)
(b) (98.37 , 99.63)
(c) (96.52 , 101.48)
(d) (97.96 , 100.04)
(e) (96.92 , 101.08)
19. How many specimens needed to compute the 95% confidence interval with the interval width of 1
calorie per gram?
(a) 7
(b) 8
(c) 15
(d) 16
(e) 62
STAT 211-200
EXAM 3- FORM A
SUMMER03
20. If you are computing the 81.98% confidence interval for  where the population distribution is normal
and the population standard deviation is known, which of the following is the corresponding critical
value?
(a) 0.915
(b) 0.933
(c) 1.34
(d) 1.57
21. If the critical value for the confidence interval of  is 0.95, which of the following is the corresponding
confidence level?
(a) 0.0500
(b) 0.1711
(c) 0.6578
(d) 0.8289
(e) 0.9500
I am interested in determining the true average price of tomatoes sold in stores per pound. I collected the
sample data and computed two confidence intervals (0.85 , 1.05) and (0.89 , 1.01) with the only difference
being the confidence level in these intervals. Answer the following 4 questions using this information.
22. If I claim that one of these intervals is 90% and the other one is 80%, which of those intervals is 80%
confidence interval for the true average price of tomatoes sold in stores per pound?
(a) (0.85 , 1.05)
(b) (0.89 , 1.01)
23. Which of the following is the sample average price of tomatoes sold in stores per pound?
(a) 0.85
(b) 0.89
(c) 0.90
(d) 0.95
(e) 0.99
24. Which of the following is the width of the interval (0.85 , 1.05)?
(a) 0.10
(b) 0.20
(c) 0.25
(d) 0.35
(e) 0.40
25. If I have also computed the 99% confidence interval additional to the 80% and 90% confidence
intervals, would the 99% confidence interval be wider or narrower than the others?
(a) Wider
(b) Narrower