201q_finalsum13.pdf

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Final Exam

QBA 201 – Summer 2013

Instructor: Michael Malcolm

Instructions: You can use a calculator and any written materials you would like in

completing this exam.

Statement of academic honesty:

This exam entirely reflects my own work. I have not received assistance from

anyone or given assistance to anyone in completing this exam

Signature: _________________________________

Name:

_____________________________________

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Multiple Choice (2 points each)

1. The power for a statistical test is

a. The probability of rejecting the null hypothesis when it is true b. The probability of rejecting the null hypothesis when it is false

c. The probability of observing the given data when the null hypothesis is true d. The probability of observing the given data when the null hypothesis is false

2. The size of a statistical test is

3. The p-value for a statistical test is

4. If the median deposit in a bank is AED 1000 but the mean deposit is AED 3000, then this means that

a. The coefficient of variation is greater than 0.33 b. The coefficient of variation is greater than 3

c. Most deposits are small, but there are a few very large deposits d. Most deposits are large, but there are a few very small deposits

5. The arrival time for an ambulance is uniformly distributed from 5 minutes to 15 minutes. If you call for an ambulance and you have already waited for 10 minutes, what is the probability that you will wait more than 12 minutes?

a. 0.08

b. 0.3

c. 0.5

d. 0.6

6. The 𝑅2 of a regression would equal 1 if there were no

a. Explained variation

b. Unexplained variation

c. Intercept

d. Severe outlier

7. If we take an iid random sample of 𝑛 observations from some population, then the sample mean is

a. An unbiased estimator of the population mean

b. A consistent estimator of the population mean

c. The efficient estimator of the population mean

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8. If two events A and B are independent, then

a. They never occur together

b. 𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴)𝑃(𝐵)

c. Both (a) and (b)

d. None of the above

9. If X and Y are random variables such that the variance of X is 7.5, the variance of Y is 6 and the covariance between X and Y is 4, then the variance of 2X + 3Y is

a. 33

b. 37

c. 84

d. 132

10. If the confidence level is reduced, then a confidence interval

a. Widens

b. Narrows

c. Stays the same as long as the sample size does not change

d. Impossible to determine

11. A regression is run using three observations of data points (𝑥, 𝑦): {(4,8), (2,5), (1,2)}. The estimated regression line is 𝑦̂ = 3 + 2𝑥. What is the sum of squared residuals for this regression line?

a. 22

b. 15

c. 8

d. 7

12. If a dataset is approximately bell-shaped and has a mean of 167, with a standard deviation of 10, then approximately 95% of the data will lie in the interval

a. [167,187]

b. [157, 177]

c. [157, 187]

d. [147, 187]

13. According to the Central Limit Theorem, the normal distribution provides a good approximation for the distribution of the sample mean

a. For any population no matter what the sample size is

b. For any population only when the sample size is large

c. For normally distributed populations only, no matter the sample size d. For normally distributed populations only, and only for large sample sizes

14. For a random variable that follows a Poisson distribution

a. The mean and the standard deviation are equal

b. The mean and the variance are equal

c. The mean and the median are equal

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15. For a standard normal random variable 𝑍, what is 𝑃(−1.30 < 𝑍 < 1.50)?

a. 0.0968

b. 0.4032

c. 0.8364

d. 0.9032

16. If we are testing at significance level 𝛼 = 0.05, which of the following p-values will lead to a rejection of the null hypothesis?

a. 0.02

b. 0.06

c. 0.10

d. Both (b) and (c) are correct

17. A random sample of 25 observations is selected from a normally distributed population. The sample

variance is 10. In a 95% confidence interval for the population variance, the upper limit is

a. 6.09

b. 17.12

c. 17.33

d. 19.35

18. The probability that a doctor will make mistake A is 0.05. The probability that a doctor will make mistake B is 0.03. The two mistakes are independent of each other. What is the probability that the doctor makes at least one mistake?

a. 0.0015

b. 0.0785

c. 0.08

d. 0.15

19. How can you tell from looking at Excel output whether a regression coefficient is significantly different from zero?

a. Look at the 𝑅2

b. Look at the adjusted-𝑅2

c. Look at the p-value

d. None of the above

20. Suppose we measure a dataset in kilograms, and we find that the standard deviation is 5 and the coefficient of variation is 40. But your supervisor wants the statistics in grams. Which is correct?

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21. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, where is the cutoff for the lowest 10% of the IQ distribution?

a. 80.8

b. 85

c. 98.5

d. 98.72

22. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what is the probability in a randomly chosen group of 100 students that the average IQ will be greater than 110?

a. Almost zero

b. 0.2514

c. 0.7486

d. Almost one

23. Which of the following is a continuous random variable?

a. The size of the soda ordered by customers at Burger King

b. The color of a student’s hair

c. The amount of milk produced by a cow in 24 hours

d. The number of employees at an automobile factory

24. A sample size of 68 is needed to form a confidence interval with a margin of error equal to 10. The standard deviation is 50. This implies that the confidence level for the confidence interval is

a. 99%

b. 97.5%

c. 95%

d. 90%

25. If the probability of making a Type I error is decreased then, for a fixed sample size 𝑛, the probability of making a Type II error

a. Increases

b. Decreases

c. Stays the same

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Problem 1 (15 points)

Professors get a series of student evaluations over many courses that they teach. Suppose that

there are three types of professors.



An excellent professor gets satisfactory evaluations 90% of the time.



A good professor gets satisfactory evaluations 75% of the time.



A bad professor gets satisfactory evaluations 40% of the time.

AUS hires a new professor. After teaching 6 classes, he received satisfactory evaluations in 5 out

of these 6 classes.

a.

What is the probability of this event if the professor is excellent?

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b.

What is the probability of this event if the professor is good?

c.

What is the probability of this event if the professor is bad?

d.

The dean begins the year believing there is a 50% chance that the professor is excellent, a

25% chance that he is good and a 25% chance that he is bad. Now the year is over. Use

Bayes’ rule to find the posterior probability that the professor is excellent.

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Problem 2 (15 points)

You are interested in the determinants of a baby’s birthweight, so you take a sample of 1388

newborn babies. You regress the baby’s birthweight (in pounds) on the following independent

variables:



INCOME = mother’s income (in thousands of dollars)



MALE = dummy variable equal to 1 if the baby is male



CIGS = number of cigarettes smoked by the mother each day during pregnancy

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a.

Write out the estimated regression equation

b.

Which of the independent variables are statistically significant determinants of a

newborn’s birthweight, at

𝛼 = 0.05

? Explain briefly.

c.

Interpret the coefficient on MALE precisely.

d.

Develop a 95% confidence interval for the estimated impact on a newborn’s birthweight

when the mother smokes 20 cigarettes a day compared to an otherwise identical mother

who does not smoke.

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Problem 3 (10 points)

You and your sister both have a goose that lays one golden egg every day. The golden egg laid

by your sister’s goose always weighs 10 grams. The weight of the golden egg laid by your goose

is random, and uniformly distributed between 8 and 13 grams.

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Problem 4 (10 points)

You are a quality control inspector. A machine in proper working condition should dispense an

average of 50 ounces of oil into each container, with a standard deviation of 8 ounces. To test

whether the machine is working properly, you randomly select 36 containers and find an average

of 48.6 ounces dispensed in each container.

a.

Is there enough evidence to conclude at a significance level of 5% that the machine is not

functioning properly?

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