STAT 211 EXAM 3 SPRING 2003
Observations on burst strength (lb/in2) were obtained both for test nozzle closure welds (X) and for production canister nozzle welds (Y). The results are shown on the following table
X: Test / 5200 / 7200 / 6100 / 7300 / 7300 / 8000 / 7400 / 7300 / 7300 / 8000 / 6700 / 8300Y: Canister / 5250 / 5625 / 5900 / 5900 / 5700 / 6050 / 5800 / 6000 / 5875 / 6100 / 5850 / 6600
The following descriptive statistics are obtained using MINITAB software.
Variable n Mean Median StDev Minimum Maximum Q1 Q3
X:Test 12 7175 7300 854 5200 8300 6825 7850
Y:Canister 12 5887.5 5887.5 317.9 5250 6600 5725 6037.5
95% confidence interval for the true mean of X’s: (6632.39 , 7717.61)
95% confidence interval for the true variance of X’s: (365988.870 , 2102325.996)
Answer questions 1 to 11 using the information above.
1. Which of the following is the estimated variance for X-Y?
(a) 263.06
(b) 536.10
(c) 1171.90
(d) 628255.59
(e) 830376.41
2. Which of the following is the estimated standard error for -?
(a) 263.06
(b) 536.10
(c) 69198.03
(d) 628255.59
(e) 830376.41
3. Which of the following is the estimated expected value for -?
(a) 1287.5
(b) 1412.5
(c) 3949.5
(d) 5887.5
(e) 7175
4. What is the point estimate for the true proportion of Y’s larger than 5900?
(a) 0.3333
(b) 0.4167
(c) 0.50
(d) 0.5833
(e) 0.6667
5. If the Y’s are drawn from a normally distributed population, which of the following is the point estimate for the P(Y>5900)?
(a) 0.2342
(b) 0.4840
(c) 0.5160
(d) 0.7658
(e) none of the above
6. If we are interested in constructing the confidence interval for the true proportion of X’s larger than 7300, do we have a large sample to construct the interval?
(a) Yes
(b) No
7. If the random sample of X’s were drawn from a normal distribution with the mean m and the variance s2, which of the following is the Maximum Likelihood Estimator (MLE) for s2?
(a) 782.83
(b) 854
(c) 60776.33
(d) 668539.67
(e) 729316
8. If the random sample of X’s were drawn from a normal distribution with the mean m and the variance s2, which of the following is the Method of Moment Estimator (MME) for m?
(a) 317.9
(b) 854
(c) 7175
(d) 7300
(e) 5887.5
9. If I claimed that the true standard deviation of X’s is 650, would you believe me by looking at the 95% confidence interval of the true standard deviation of X’s?
(a) Yes. 650 falls in the confidence interval
(b) No. 650 falls in the confidence interval
(c) Yes. 650 does not fall in the confidence interval
(d) No. 650 does not fall in the confidence interval
10. If I claimed that the true mean of X’s is 7300, would you believe me by looking at the 99.75% confidence interval for the true mean of X’s?
(a) Yes. 7300 falls in the confidence interval
(b) No. 7300 falls in the confidence interval
(c) Yes. 7300 does not fall in the confidence interval
(d) No. 7300 does not fall in the confidence interval
11. When I constructed the confidence interval for the true mean of X’s in question 10, which of the following critical values that I have used?
(a) ta/2;n-1
(b) za/2
(c) c2a/2;n-1
(d) c2(1-a/2);n-1
(e) both (c) and (d)
12. Which of the following is the critical value for the 99% confidence interval for the true mean of X when X’s are drawn from a normal population distribution with the size 23 and unknown population standard deviation?
(a) 2.575
(b) 2.603
(c) 2.807
(d) 2.819
(e) 2.925
13. In which of the following cases, you can compute the large sample confidence interval for the true proportion?
(a) n>40
(b) n=100, =0.02
(c) n=100, p=0.20
(d) none of the above
(e) all of the above
14. What is the confidence level for the interval ?
(a) 0.0064
(b) 0.0128
(c) 0.9936
(d) 0.9968
(e) 0.9872
15. If you increase the sample size by a factor of 81 keeping everything else the same, what happens to the width of the confidence interval for the true mean?
(a) Reduced by factor 1/81
(b) Reduced by factor 1/9
(c) No change
(d) Increased by factor 9
(e) Increased by factor 81
Suppose that , and are estimators of the parameter . We know that , , , and . Answer the next 2 questions using this information.
16. Which of the following is the complete answer for the unbiased estimators of ?
(a) Only is an unbiased estimator for
(b) Only is an unbiased estimator for
(c) Only is an unbiased estimator for
(d) and are unbiased estimators for
(e) , and are unbiased estimators for
17. Which of the following is the minimum variance unbiased estimator for ?
(a)
(b)
(c)
(d)
(e)
18. If I argue that the only difference between the confidence intervals (50,105) and (25,130) for m is the confidence level and everything else is the same, which of the following is incorrect?
(a) If the claimed m falls in the first interval, it definitely falls in the second interval
(b) If the claimed m falls in the second interval, it definitely falls in the first interval
19. Which of the following is the complete answer for the confidence level of the interval ? (your answer should be in terms of whatever table gives you)
(a) 0.0310
(b) Between 0.025 and 0.05
(c) Between 0.95 and 0.975
(d) 0.95
(e) 0.969
20. 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 incorrect?
(a) The confidence interval becomes narrower
(b) The width of the confidence interval becomes smaller
(c) The bound on the error estimation becomes larger
(d) The true standard deviation does not change
(e) Sample size does not change
Answer Key:
1.e 2.a 3.a 4.a 5.b 6.b 7.d 8.c 9.a 10.a 11.a 12.d
13.d 14e 15.b 16.d 17.e 18.b 19.e 20.c