A Marketing Manager at Very Big Machines Wants to Determine Probabilities for the Number
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STAT 211 AUGUST 14, 2002
You have 2 hours to complete this exam. You can only use your own calculator , 3 pages formulas (front and back can be used) and t, z, chisquare, F tables. There is penalty of 5 pt. if you separate your exam with any reason.
There are 25 questions (100 pts. total) and there is no partial credit on this exam.
If you did not mark your final answer on your scantron, your answer will be counted incorrect.
If you caught cheating, you will get a grade of zero. Good Luck.
FINAL EXAM
1. An assembler of electric fans uses motors from two sources. Company A supplies 90% of the motors and company B supplies the other 10% of the motors. Suppose it is known that 5% of the motors supplied by company A are defective while 3% of the motors supplied by company B are defective. An assembled fan is found to have a defective motor. What is the probability that this motor was supplied by company B? (a) 0.003 (b) 0.05 (c) 0.0625 (d) 0.9375 (e) 0.997
2. Seventy percent of all cattle are treated by an injected vaccine to combat a serious disease. The probability of recovery from the disease is 1 in 20 if untreated and 1 in 5 if treated. If an infected cow was recovered, what is the probability that the cow received the preventive vaccine? (a) 0.1657 (b) 0.3373 (c) 0.6627 (d) 0.7000 (e) 0.9032
3. Suppose that it is known that 1 out of 10 undergraduate college textbooks is an outstanding financial success. A publisher has selected 10 new textbooks for publication. What is the probability that exactly one will be an outstanding financial success? (a) 0.0387 (b) 0.1000 (c) 0.3874 (d) 0.6126 (e) 0.9613
4. Which of the following is not a legitimate null hypothesis? (a) =20 (b) p 0.10 (c) 13 (d) p < 0.10 (e) = 13 The concentration of active ingredient in a liquid laundry detergent is thought to be affected by the type of catalyst used in the process. Ten observations on concentration are taken from each catalyst, and the data are shown below: Catalyst 1 57.9 66.2 65.4 65.4 65.2 62.6 67.6 63.7 67.2 71 Catalyst 2 66.4 71.7 70.3 69.3 64.8 69.6 68.6 69.4 65.3 68.8 Variable N Mean Median TrMean StDev SE Mean Catalyst 1 10 65.22 65.40 65.41 3.44 1.09 Catalyst 2 10 68.380 69.050 68.413 2.268 0.717
Let 1 and 2 denote the true concentration recorded for Catalyst 1 and Catalyst 2, respectively. Answer questions 5 to 7 using this information.
5. I would like to test if the true standard deviations being the same in both catalyst types. Which of the following would be your conclusion? (Use =0.10) (a) The test statistics is 1.5168 and true standard deviations are different in both catalyst types (b) The test statistics is 1.5168 and true standard deviations are the same in both catalyst types (c) The test statistics is 2.3006 and true standard deviations are different in both catalyst types (d) The test statistics is 2.3006 and true standard deviations are the same in both catalyst types
6. I have also looked at the previous studies and found out that the true variance for the Catalyst 1 is 11. I would like to check if this is true. Which of the following would be your conclusion for this test? (Use =0.05) (a) The test statistics is 2.815 and true variance for catalyst 1 is not 11 (b) The test statistics is 2.815 and true variance for catalyst 1 is 11 (c) The test statistics is 9.682 and true variance for catalyst 1 is not 11 (d) The test statistics is 9.682 and true variance for catalyst 1 is 11
7. What percent of the data for Catalyst 1 is less than its median? (a) 0.30 (b) 0.40 (c) 0.50 (d) 0.60 (e) 0.70
8. If the P-value is 0.25, which of the following is correct?
(a) Reject H0 with =0.05
(b) Fail to reject H0 with =0.30
(c) Reject H0 with =0.01
(d) Fail to reject H0 with =0.05
(e) Reject H0 with =0.10
9. If the test statistics is z=-0.7 and n=9 for the lower tailed test, which of the following is the P-value? (a) 0.242 (b) 0.420 (c) 0.580 (d) 0.758 (e) none of the above
10. If the test statistics is t=-0.7 and n=9 for the lower tailed test, which of the following is the P-value? (a) More than 0.10 (b) Between 0.005 and 0.10 (c) Between 0.001 and 0.005 (d) Between 0.0005 and 0.001 (e) Less than 0.0005 To obtain information on the volume of freight shipped by truck over a particular interstate highway, a state highway department monitored the highway for one hour periods randomly selected throughout a one- month period. The number of heavy-duty trailers per hour is approximately normally distributed with =50 and =7. Answer questions 11 to 13 using this information.
11. What is the probability that the number of trucks for one-hour period would exceed 60? (a) 0.0021 (b) 0.0764 (c) 0.5000 (d) 0.9236 (e) 0.9979
12. What is the probability that average number of trailers for a four-hour period will be larger than 60? (a) 0.0021 (b) 0.0764 (c) 0.5000 (d) 0.9236 (e) 0.9979
13. What is the probability that the total number of trucks for a four-hour period would exceed 180? (a) 0.0021 (b) 0.0764 (c) 0.5000 (d) 0.9236 (e) 0.9979
14. We computed the probability of the test statistics fall in the rejection region when the false null hypothesis is tested. Which of the following we computed? (a) =P(reject H0 when H0 is true) (b) = P(fail to reject H0 when H0 is false) (c) Power=1- (d) 1- (e) all of the above
15. Which of the following is incorrect about simple regression? (a) Testing the slope being zero is the same as testing the correlation coefficient being zero (b) We have one dependent variable and many independent variables (c) The R2 explains the percent variation in the dependent variable explained by the model (d) The correlation coefficient can be any number between –1 and 1 (e) The sign for the slope will be the same as the sign for the sample correlation coefficient
16. What is today? (a) Monday (b) Tuesday (c) Wednesday (d) Thursday (e) Friday In large classes instructors sometimes use different forms of an examination. When average scores for different forms are calculated, students who received the form with the lowest average score complain that their examination was more difficult than the others. Analysis of variance can help determine whether the variation in mean scores is larger than would be expected by chance. The following data is used for the analysis Form sample size sample mean sample standard deviation 1 79 31.78 4.45 2 81 32.88 4.40 3 81 34.47 4.29 and the following Analysis of variance (ANOVA) table is obtained.
Source of Variation df SS Between 2 292.01871 Within 238 4566.28004 Total 240 4858.29876
Answer question 17 to 25 using the information above
17. Which of the forms has the lowest average score? (a) Form 1 (b) Form 2 (c) Form 3 (d) Forms 2 and 3 (e) Forms 1 and 3
18. Which of the forms has the most variation in their score? (a) Form 1 (b) Form 2 (c) Form 3 (d) Forms 2 and 3 (e) Forms 1 and 3
19. How many test forms compared? (a) 0 (b) 1 (c) 2 (d) 3 (e) 4
20. Which of the following is the correct null hypothesis?
(a) H 0 : 0
(b) H 0 : 1 2 0
(c) H 0 : 1 2
(d) H 0 : 1 2 3 0
(e) H 0 : 1 2 3
21. Which of the following is the point estimate for the constant variance 2? (a) 19.186051 (b) 146.009355 (c) 292.01871 (d) 4566.28004 (e) 4858.29876 22. Which of the following is the F statistics for ANOVA? (a) 3.45 (b) 5.84 (c) 6.57 (d) 7.61 (e) 9.15
23. Which of the following is the approximate correct critical value using =0.05 for ANOVA? (a) 2.31 (b) 2.33 (c) 3.04 (d) 4.71 (e) 7.15
24. If you reject the null hypothesis, which of the following would be your conclusion? (a) The students took the exam with Form 1 will complain (b) The students took the exam with Form 2 will complain (c) The students took the exam with Form 3 will complain (d) None of the students will complain (e) It is not possible to make a decision
25. What is the total number of data used in this experiment? (a) 79 (b) 81 (c) 238 (d) 240 (e) 241
Answer Key: 1. c 2.c 3.c 4.d 5.d 6.d 7.b 8.d 9.a 10.a 11.b 12.a 13.d 14.c 15.b 16.c 17.a 18.a 19.d 20.e 21.a 22.d 23.c 24.a 25.e