Exam Sample II STAT 211
(Fall 2010)
Name :
Student ID :
You have 75 minutes to complete this test.
You may use the provided sheets, all appropriate tables (if any) and a calculator.
If I provide partial resultsassume they are correct and use them even if they are not.
If there is no correct answer or if multiple answers are correct, select the best answer.
This test consists of 20 questions. Make sure you have all questions and Good luck!
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1. Household electricity bill is $100 per month on average, with variance 400. We sample 100
families, what is the probability that the average we calculate from these 100 families is
larger than $105?
A. 0.4880
B. 0.1056
C. 0.8944
D. 0.9938
E. 0.0062
2. Assume X and Y are two independent standard normal random variables. What is the
mean of X + Y ?
A. 2.
B. 0.
C. 2.
D. insucient information to calculate.
E. none of the above.
3. Assume X and Y are two independent standard normal random variables. What is the
standard deviation of X + Y ?
A. 2.
B. 0.
C. 2.
D. insucient information to calculate.
E. none of the above.
4. Suppose the joint pdf of X and Y is p(x, y ) =
of Y ?
A.
2
1
ey .
C.
2
1 ex .
2
D.
What is the marginal pdf
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3
e 4 x .
2
B.
1 x2 +4xy 5y 2
.
e
2
1
ey .
E. None of the above is correct.
5. Continue from the previous problem. What is the marginal pdf of X ?
A.
2
1 ex /5 .
5
2
B.
C.
D.
1 x2 /5
.
e
2
1
e5x .
2
1
ex .
E. None of the above
6. Continue from the previous problem. Are X and Y independent of each other?
A. Unable to determine.
B. Yes.
C. No.
D. They are correlated, but can be independent.
E. They are uncorrelated, but can be dependent.
7. Assume X is a random variable following a Gamma distribution with parameters = 1
and = 1. Assume the random variable Y also follows a Gamma distribution with
parameters = 2 and = 1. We further assume that X and Y are independent of each
other. What is the probability of X > Y ?
A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4
8. Which one of the following is not a statistic?
A. The median of the observations.
B. The mean of the data.
C. The sample variance.
D. The population mean.
E. The maximum of the observation.
9. To decrease the length of a condence interval, we can
A. increase the condence level.
B. increase the sample size.
C. increase the variance.
D. increase the mean.
E. none of the above.
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10. You sample 400 seniors about their starting salary and nd that x = 40, 000 and that
s = 10, 000. Construct a 99% condence interval for .
A. 40, 000 1163
B. 40, 000 12880000
C. 40, 000 64.4
D. 40, 000 1288
E. We need to know to answer this question.
11. In a sample of 200 TAMU students, 160 of them have never been to New York city. A
99% condence interval for the proportion of TAMU students who have never been to New
York city is:
A. [0.980,1.000].
B. [0.727,0.873].
C. [0.950,0.990].
D. [0.711,0.889].
E. none of the above.
12. In calculating the condence interval for population mean () with unknown , we can
A. Use central limit theorem for small sample size.
B. Use sample variance only for large sample size.
C. Use student-t a distribution to replace normal for small sample size.
D. Use a student-t distribution to replace normal for small sample size if the original
observations are normal.
E. All of the above.
13. Which of the following is not a valid statistical hypothesis?
A. HA : = 1.
B. HA : (1 /2 ) = 1.
C. HA : x1 = x2
D. HA : 1 = 42 +
E. All are valid.
14. In a hypothesis testing, if we want to increase the power of the test, we can
A. decrease the type I error allowed.
B. increase the type II error allowed.
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C. increase the type I error allowed.
D. decrease the sample size.
E. none of the above.
15. In a hypothesis testing, if we want to decrease the type II error of the test, we can
A. decrease the type I error allowed.
B. decrease the power of the test.
C. decrease the sample size.
D. decrease the level of the test.
E. None of the above.
16. Which statement about p-value of population mean is correct?
A. p-value decreases if sample size increases.
B. p-value decreases if increases.
C. p-value decreases if increases.
D. p-value decreases if increases.
E. None of the above.
17. We test H0 : = 100 vs HA : < 100. Our p-value for the test is 0.0227. At = 0.03,
A. we fail to reject H0 .
B. we fail to reject H0 , with type I error 0.03.
C. we reject H0 with 0.0227 type II error.
D. we reject H0 with 0.0227 type I error.
E. we know we will reject H0 at = 0.02.
18. Concerned about the global warming issue, the average monthly temperature of the past
three years of Shanghai is analyzed in comparison with its historical average. The average
we calculated based on the three years data is 20C . It is known that historically, the
average temperature in Shanghai is 18C with sample variance 49C 2 . Based on this, at
level = 0.05, would you think the city was warmer in the past three years than usual?
A. We test H0 : t = 18, HA : t = 18. We conclude the city was warmer in the past 3
years than usual.
B. We test H0 : t = 18, HA : t > 18. We conclude the city was warmer in the past 3
years than usual.
C. We test H0 : t = 18, HA : t < 18. We conclude the city was warmer in the past 3
years than usual.
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D. We test H0 : t = 18, HA : t > 18. We conclude the city was not warmer in the past 3
years than usual.
E. We test H0 : t = 18, HA : t < 18. We conclude the city was not warmer in the past 3
years than usual.
19. In the above problem, if you want to achieve a power of 80% in detecting a 2C increase of
the average temperature, how many more months measurements would you need?
A. 75
B. 76
C. We can never detect such a small increase with such a big variation.
D. 40
E. 39
20. We randomly sampled 100 seabasses from the gulf and found that 60% of them are females.
Do you think the male/female seabass populations are about equal in the gulf?
A. At level = 0.05, we would believe they are not equal.
B. At level = 0.03, we would believe they are not equal.
C. At level = 0.05, we would believe they are equal.
D. At level = 0.01, we would believe there are more females than males.
E. We need to sample more seabasses to answer the question.
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