Res Econ Exam 2

1. What does the correlation coefficient tell us? 1. The sign and degree of apparent linear association between two variables 2. The degree of apparent quadratic association between two variables 3. The product of variances of two variables 4. The variance of a variable 5. The 10th standardized moment of a variable about its mean

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2. Why might we prefer to look at a correlation coefficient rather than covariance? 1. Correlation coefficient is unitless while covariance has weird units. 2. Correlation coefficient can be compared across different variable pairs. 3. Correlation coefficient has an easy interpretation. 4. All of the above.

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3. Refer to graphic #1. What is the correlation coefficient between SnoAmt and LiftOps? 1. 0.128 2. 0.242 3. 0.207 4. 0.172

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4. What is the difference between kurtosis and excess kurtosis? 1. Kurtosis is 3 for a normal distribution; excess kurtosis is 0 for a normal distribution (because it subtracts 3!). 2. Kurtosis is normal kurtosis; excess kurtosis is the part you don't need. 3. Kurtosis is 1,000,000 for normal distributions; excess kurtosis is 1,000,000,000 for normal distributions. 4. Kurtosis is associated with normal distributions; excess kurtosis results when the distribution is not normal.

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5. How many moments can be calculated for a given distribution? 1. 10 2. 4 3. 2 4. Infinitely many. But usually we stop at 2 (variance), sometimes 3 (skewness) or 4 (kurtosis), unless we're self-deluded and megalomaniacal options traders, who might take it all the way to 10 or more.

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6. What is the point of estimating the 3rd and 4th moments of a distribution about its mean? 1. There never is one. 2. Sometimes it is useful to test your data for non-normality, but you'd better have a darn good reason to do so.

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7. What is another name for the standardized 3rd moment about a distribution's mean? 1. Kurtosis coefficient 2. Skewness coefficient 3. Variance 4. Standard deviation 5. Mean

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8. What is another name for the standardized 4th moment about a distribution's mean? 1. Kurtosis coefficient 2. Skewness coefficient 3. Variance 4. Standard deviation 5. Mean

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9. What is another name for the un-standardized 2nd moment about a distribution's mean? 1. Kurtosis coefficient 2. Skewness coefficient 3. Variance 4. Standard deviation 5. Mean

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10. What is another name for the un-standardized 1st moment of a distribution about 0? 1. Kurtosis coefficient 2. Skewness coefficient 3. Variance 4. Standard deviation 5. Mean

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11. What is the ludic fallacy? 1. Attempting to apply empirical or even classical probability tools to fundamentally subjective probability situations 2. The turkey problem of prediction 3. Assuming that the "rules of the casino" always apply to real-life situations 4. All of the above

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12. Refer to Table #1. What is the probability that a randomly selected student did NOT get an A? 1. 0.217 or 21.7% 2. 0.783 or 78.3% 3. or 100% 4. or 0%

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13. Refer to Table #1. What is the probability that a randomly selected student is a senior OR got a B? 1. 0.076 or 7.6% 2. 0.056 or 5.6% 3. 0.02 or 2% 4. 0.002 or 0.2% 5. 0.074 or 7.4%

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14. Refer to Table #1. What is the probability that a randomly selected student got an A or an A-? 1. 0.783 or 78.3% 2. 0.073 or 7.3% 3. 0.856 or 85.6% 4. 1.00 or 100% 5. 0.50 or 50%

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15. Refer to Table #1. What is the probability that a randomly selected student got a B on exam 1, GIVEN THAT HE OR SHE IS A SOPHOMORE? 1. 0.019 or 1.9% 2. 0.015 or 1.5% 3. 0.773 or 77.3% 4. 0.02 or 2%

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16. A die is thrown 10 times, and a 1 is rolled every single time! What is the probability of rolling a 1 on the 11th row? 1. 1/6, just like on all the other rolls. Die tosses are independent events. 2. It drops down a bit, since the likelihood of getting 11 1's in a row is so small. 3. 5/6 4. 0 5. 1

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17. You flip a coin 5 times in a row. What is the chance of getting heads for all 5 coin tosses (hint: coin tosses are independent events)? 1. 0.5 or 50% 2. or 100% 3. or 0% 4. 0.03125 or 3.125%

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18. Suppose 1.41% of taxpayers in your income bracket get audited by the IRS each year. What are the odds against your being audited this year, roughly? 1. 0.0141 or 1.41% 2. 0.9859 or 98.59% 3. 1 to 70 4. 70 to 1

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19. The odds against Fred the race horse winning the next race are 4 to 1. What is the probability of Fred winning the next race? 1. 0.25 or 25% 2. or 100% 3. 0.5 or 50% 4. 0.2 or 20%

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20. Use Bayes Theorem to help you answer this question. Suppose the following: 1% of women have breast cancer (99% do not). 80% of mammograms detect breast cancer when it is there (20% miss it). 9.6% of mammograms detect breast cancer when it's not there (90.4% correctly say no cancer). What is the probability of a woman having cancer, given that her mammogram results came back positive? 1. 0.096 or 9.6% 2. 0.904 or 90.4% 3. 0.20 or 20% 4. 0.078 or 7.8% 5. 0.922 or 92.2%

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21. How many different samples of size 5 can be drawn from a population of size 10 (without replacement)? 1. 94,212,065,332 2. An infinite number of different samples 3. 415 4. 82 5. 252

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22. True or False? There is a Bayesian version of every classical/frequentist technique you will learn in this class. 1. True 2. False

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23. You pull out a random ball from a bag with 30 red balls and 70 green balls, then put it back. You do this a total of 6 times. What is the expected number of red balls? 1. Not enough information given 2. 3 red balls 3. 6 red balls 4. 1.8 red balls 5. 30 red balls

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24. You pull out a random ball from a bag with 30 red balls and 70 green balls, then put it back. You do this a total of 6 times. What is the standard deviation of number of red balls? 1. Not enough information given 2. 1.12 red balls 3. 6 red balls 4. 1.8 red balls 5. 30 red balls

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25.You pull out a random ball from a bag with 30 red balls and 70 green balls, then put it back. You do this a total of 6 times. What is the probability of getting 1 or fewer red balls? 1. 0.49 2. 0.420175 3. 1.00 4. 0.00 5. 0.12

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26. You have a box with 200 balls in it. There are 100 red and 100 black. You take out a ball. It is black. You take out a second ball, without replacing the first. What is the probability the 2nd ball is also black, given the first was black? 1. 0.5 2. 0.25 3. 0.4975 4. 1.00 5. 0.00

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27. When might you need to use a Possion discrete PDF? 1. To model the number of customers per hour at my bank 2. To model number of website users per minute 3. To predict the likelihood that there will be 20,000 or more customers visiting my website in a single minute 4. To predict the likelihood of getting above a certain threshold number of customers in an hour at my bank 5. All of the above

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28. Why do we care about the binomial and/or hypergeometric discrete PDFs in statistics? 1. We don't 2. They tell us what we can expect to see when we sample characteristics of things/people 3. They tell us the probability that we will get a certain number of things/people with a certain characteristic in our sample 4. They help us guess what percentage of a population has some characteristic 5. B, C, and D

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29. We take a sample (without replacement) of 400 students from the population of 410 and see how many are male. Can we use the binomial PDF to approximate the probability that we get 200 males in our sample? 1. Yeah, we can always use the binomial 2. Nope. N is too close to n 3. Not enough information given

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30. What is the total area under any PDF, discrete or continuous, hypothetical or empirical? 1. 0.5 2. 1.0 3. 100 4. 0.68 5. It depends on the PDF

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31. Can you use the normal distribution to get the probability that a NON-NORMALLY distributed variable X falls in some range? 1. HELL, NO. 2. No, but you can approximate it if X is approximately normal. 3. Sure. You can use it for any continuous CRV. 4. A is technically correct, but B is also true.

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32. What is the difference between an empirical PDF and a hypothetical PDF (such as the normal)? 1. The empirical represents a finite population while the hypothetical represents an infinite population. 2. The empirical represents an observed distribution while the hypothetical represents a theoretical observation-generating rule. 3. The empirical represents something that physically exists, while the hypothetical does not. 4. All populations are distributed normally. 5. A through C, but not D.

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33. We always know how reality generates what we observe, so we can always safely use a hypothetical PDF such as the normal for any statistical problem, which is fortunate because computers do it for us, so we don't even have to think about it. 1. TRUE 2. FALSE

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34. According to Brent, what are the big questions you need to keep in the back of your mind when using statistics? 1. When can we use a hypothetical PDF to make reasonable guesses about reality? 2. When does a hypothetical PDF make a bad approximation to the way reality actually generates what we observe? 3. If we aren't sure whether or not we know, is there a way we can make a decision that is robust to that uncertainty? 4. All of the above

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35. According to Brent, what is the #1`most important skill in statistics (and pretty much everywhere else in life)? 1. Knowing what you do not know 2. Understanding the normal distribution 3. Knowing how to use the Z table 4. Knowing how to use a variety of statistical software programs 5. Understanding theoretical statistics and calculus perfectly, without the ability to think critically about when they do and do not provide a useful approximation to the real world.

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36. Use the Z table to help you answer the following question. Suppose X ~ N(150,4). What is P(149 < X < 151)? 1. 0.5987 2. 0.4013 3. 0.50 4. 0.9918 5. 0.1974

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37. Use the Z table to help you answer the following question. Suppose X ~ N(150,4). What is P(X > 151)? 1. 0.5987 2. 0.4013 3. 0.50 4. 0.9918 5. 0.1974

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38. What is the probability that a randomly selected value from a distribution is greater than the 5th percentile? 1. 0.05 2. 0.95 3. 0.50 4. 0.00

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39. Use the Z table to help you answer the following question. Suppose X ~ N(150,4). What is the 75th percentile value of X? 1. 142 2. 147 3. 153 4. 150 5. 146

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40. Use the Z table to help you answer the following question. Suppose X ~ N(150,4). What is the IQR for X? 1. 142 2. 153 3. 147 4. 6 5. 3

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