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 n Mean Median TrMean StDev SE Mean
X:Births 51 79366 54318 64220 93998 13162
Y:Deaths 51 47958 34066 41493 48872 6843
U:total migration 51 28418 9430 17383 59526 8335
Variable Minimum Maximum Q1 Q3
X:Births 6035 529610 18942 85356
Y:Deaths 3142 234012 12831 57544
U:total migration -24436 299015 1507 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 l?
(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
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, /5 and /4 are the unbiased estimators of the parameter . We know that , , and . Which of the following is the minimum variance unbiased estimator for ?
(a) /5
(b) /4
(c)
(d) 2
(e)
X and Y are the continuous random variables with the joint pdf,
The marginal pdf of X is calculated as
E(XY)=1/3 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 m (true average calories per gram of a cement mixture) and the standard deviation s=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
18. Which of the following is the 95% confidence interval for m?
(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
20. If you are computing the 81.98% confidence interval for m 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 m 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