The choice denotes None of These Answers. Give exact answers unless otherwise specified. Good luck, and have fun! 1. Senator Chuck Grassley (R-IA) tosses a fair coin until he gets tails three times. In terms of 4, what is the probability that the third tail occurs on the 4 67 toss? A. (4 1)(4 2) 2 :;< B. (4 1)(4 2) 2 : C. 4(4 1) 2 : D. 4(4 1) 2 :;< 2. Suppose > is a random variable. What is @(> A ) if @(>) = 5, and DEF(>) = 2? A. 29 B. 29 C. 25 D. 27 3. Representative Elise Stefanik (R-NY) and her fiancée Matthew want to have 3 children. However, if none of the 3 is a girl, they will try again. If they still don t get a girl, they will try only once more. If the random variable > denotes the number of children the couple will have following this scheme, then what is the expected value of >? A. 7/2 B. 51/16 C. 27/8 D. 4 4. The daily number of Cheerios eaten by politicians in Washington turns out to be normally distributed with a standard deviation of 37 Cheerios. You re trying to use this data to estimate the population mean of Cheerios eaten by senators within ±10 Cheerios with 95% confidence. What is the smallest possible size of the sample you must take? A. 52 B. 47 C. 53 D. 45 5. A simple random sample of 40 senators was taken regarding the number of bills they ve sponsored or cosponsored that have been enacted into law, resulting in the following 95% confidence interval: (83, 102). Which of the following is the most valid interpretation of this interval? A. If the procedure were repeated many times, 95% of the sample means would be between 83 and 102. B. The probability that the population mean number of bills enacted per senator is between 83 and 102 is.95. C. 95% of the sampled senators have a number of bills enacted that is between 83 and 102. D. If the procedure were repeated many times, 95% of the resulting intervals would contain the population mean number of bills enacted into law for each senator. E. 95% of the population of senators have passed between 83 and 102 bills. 6. In a recent poll, 500 registered voters were asked the following question: Of all the Republicans currently serving in the Senate, would John McCain (R-AZ) make the best apple pie? Find the 95% confidence interval for the true proportion of registered voters who think John McCain would make the best apple pie if 436 of the 500 people polled answered in the affirmative. (Round to 4 decimals.) A. (.8427,.9013) B. (.8420,.9020) C. (.7963,.9477) D. (.8550,.8890) 1
7. If the following is true about sets X and Y: >Z = 28, [Z = 42, S x = 12, S y = 25, r =.6; What is the value of the residual when X = 5 and Y = 20? A. 7.25 B. 6.75 C. -7.25 D. -6.75 8. Set A contains integers { 9, 8, 3, 10, X }; Set B contains integers { 2, 5, 0, 7, 6, [}. If _ is the median of Set A and ` is the mode of Set B, and _ a is a factor of 34, what is the value of [ if > is negative? A. -2 B. 0 C. 1 D. 8 Questions 9 and 10: Kanye is preparing for his 2020 presidential bid. In order to convince the leaders of the newlyformed YMCMB Party that he is a viable candidate, he tries to prove that he would fare better in a general election than Drake would. 9. While he knows he s the better candidate, Kanye wants to check how likely it is that this test will determine that he is definitively better. What is Kanye looking for if he wants to know the probability that the test will (correctly) reject the claim that he and Drake are effectively equivalent in the eyes of the public? A. Type II error B. Power C. Type I error D. p-value 10. Kanye doesn t trust the establishment. He doesn t think their test is powerful enough. Which of the following would lead to an increase of the power of the establishment s test? I. An increase in the standard deviation II. An increase in the sample size III. Increasing the significance level IV. An increase in the size of the difference between means A. II, IV B. I, II, III C. II, III D. II, III, IV 2
11. Representative Al Lawson (D-Tallahassee) wants to know how many people in all 8 counties in his district voted for him in the last midterm election. He printed out a list of the counties and their respective vote counts in ascending order. However, he spilled his coffee on the list and now several values have been smudged. He can still see the actual numbers from 3 of the counties, and he has the printout listing the 5-number summary of the distribution. County Number of Votes Columbia a Hamilton 393 Min = 131 Gadsen b Q1 = 524 Baker 917 Med = 1,179 Jefferson c Q3 = 1,965 Leon d Max = 2,489 Duval 2,227 Madison e Using this information, determine how many people in total voted for Representative Lawson in the last midterm election. A. 9,432 B. 9,825 C. 9,956 D. 10,087 12. Variable X is a uniformly distributed random variable on the interval (0,10). What is fg> + <i j 7l? A. 1/2 B. 7/10 C. 4/5 D. 1/5 13. Senator Claire McCaskill (D-MO) always brings 8 apples to work. Whenever important legislation is voted on, she eats 4 randomly chosen apples right beforehand to sharpen her focus. Unbeknownst to her, however, her rival, Senator Roy Blunt (R-MO), has taken 3 of her apples and swapped them out with identical bad apples, which are sure to make her too sick to vote on the important piece of legislature if she even eats just one, or so he thinks (Secretly, Claire McCaskill has slowly and purposefully built up immunity to toxins of every variety for situations like this.) That being said, what is the expected number of bad apples she will eat before the upcoming vote? A. 1.33 B. 1.5 C. 1.66 D. 2 14. Its a well known fact that the number of Lucky Charms a senator of Congress eats in any given day follows a normal distribution. If there's a 5% chance a senator has eaten less than 24 Lucky Charms, and a 10% chance the senator has eaten more than 42 Lucky Charms on any given day, what is the mean number of Lucky Charms for this senator? (Round to 2 decimals.) A. Not enough information B. 34.12 C. 33.00 D. 34.64 3
Questions 15 and 16: Worried about political fallout from his recent decisions as Secretary of Energy, former Governor Rick Perry (R-TX) decides to go on another TV show to help increase his approval rating. Instead of Dancing with the Stars again, Perry decides to go on The Monty Show, a new probability-based game show. 15. The show opens with Perry and the show s host, Monty, standing next to three boxes labeled A, B, and C. Only Monty himself knows what is inside each box. Monty tells Perry that one of these boxes contains $5,000, and the other two contain nothing. He asks Perry to place his hand on a box of his choice. Perry strides across the stage and places his hand firmly on Box B. Then, with a knowing smile, Monty opens Box A to reveal that it is empty. Will you stay with Box B, or switch to Box C? queries Monty. Having read up on the infamous Monty Hall problem beforehand, Governor Perry confidently switches to Box C. To the nearest dollar, how much greater is the expected value of Box C than Box B? A. $1,667 B. $2,500 C. $833 D. $0 16. Going into the final challenge, Perry has $12,000. Monty shows Perry four boxes (labeled A, B, C, and D), and tells him that one contains $10,000, but one contains a red card that will make him lose all of his money. (The other two are empty). Monty asks Perry to place his hand on a box of his choice (he chooses Box A). Then, Monty opens Box B to reveal that it is empty. He then tells Perry that Box D is definitely not empty. Perry has a choice: he can open Box A, switch to Box C or D, or he can walk away and keep the money he has. If Governor Perry wants to choose the option with the highest expected value, what should he do? A. Open Box A B. Open Box C C. Open Box D D. Walk away 17. You and 5 of your friends are standing in a room. If we assume Birthdays are uniformly distributed, what is the probability at least two of you share a Birthday? (assume 365 days a year, no Feb. 29 th ) (Round to five place values.) A..01362 B..02714 C..01633 D..04046 18. You and your friends (the same 5 from last problem) are now getting bored and so they each pull out a die (you didn t get one). What s the probability that when they roll their 5 dice, exactly 3 of them turn up the same? A. 235 1296 B. 123 648 C. 31 162 D. 125 648 19. The number of people who have been at each meeting Representative Tom Cotton (R-AR) has attended today is listed in data set S, where S = {2, 3, 5, 8, 13, 21, 34, 55, 89, 144}. Find the Standard Deviation of S. A. 5 3130 6 B. 46.622 C. 2 13585 5 D. 263010 11 4
20. TargetSmart Communications is a political research and consulting firm trying to determine the proportion of voters who will consider voting Yes on a referendum that will be on the ballot in the upcoming midterm election. They took an SRS of 100 people in New Hampshire s 1 st District asking whether or not they would vote in favor of the referendum. From this data, they produced a confidence interval of (.42,.48) for the proportion of people in the district who would vote Yes. If they had increased their sample size to 300 people and still came up with the same sample proportion, what would the resulting confidence interval be? (Round to 4 decimals.) A. (.4288,.4712) B. (.4327,.4673) C. (.4350,.4650) D. Need to know the confidence level 21. Senator Sheldon Whitehouse (D-RI) is polling to know whether to vote yes or no on an upcoming piece of legislature to outlaw Nickelback concerts in Rhode Island. He randomly samples 56 of his book club buddies and 38 of them say yes. He randomly samples 56 of his badminton bad-boys and 45 of them say yes. If Senator Whitehouse runs a statistical test to determine if there s a difference in proportion between the two groups, find the value of the standard deviation used to run the statistical test to 5 decimal places. A..08194 B..08278 C..08188 D..08234 22. Senators, in their spare time, have to stay fit. Of the 70 senators that do yoga, Zumba, or Pilates or some combination of the three exactly 40 do yoga, 35 do Zumba, and 30 do Pilates. If only 15 of the senators are involved in all three, how many senators do just two of the exercise programs? A. 2 B. 5 C. 10 D. 12 23. Given f(p) = 3/10, f(q) = 3/5, and f(p q) = 1/3, what is f(q p)? A. 1/4 B. 1/3 C. 2/3 D. 3/4 24. During long filibusters, senator Mike Lee (R-UT) is known to try to stump his colleagues with a math problem to pass the time. For this one, he picks three integers, E, s, and t, where E < s < t. He then defines Set > as all integers from E to s, inclusive, and Set [ as all integers from s to t, inclusive. Similarly, v is the set of all integers from E to t, inclusive. He tells them, If the median of Set > is w s, and the median of Set [ is y t. What fraction of t is the median of v? x z A. 3/8 B. 1/2 C. 11/16 D. 5/7 5
For questions 25-26 refer to the following table, produced from an SRS recording the participants votes in the most recent election and their respective party affiliations. Rep. Dem. Total Rep. voter 403 36 439 Dem. voter 23 327 350 Total 426 363 789 25. What is the probability that a randomly chosen voter from this sample voted for the opposing party? A. 426/8591 B. 46/8591 C. 23/713 D. 59/789 26. Find the p-value for the claim that the rate of cross-party voting (casting a vote for the opposing party) is independent of party affiliation, rounded to four significant figures. A..1937 B..3874 C..1909 D..3818 27. You are trying to ask your teacher what score you got on your test, but they ve decided to only give you the statistics of where you fell in the class. If you are told the class mean was 73, the standard deviation was 5, and your z-score for the test was 1.4. What was your score on the test? A. 80 B. 84 C. 86 D. 90 28. The regression line { = 6 5 is based on five pieces of data. The five values of the independent variable are 51, 92, 61, 75, and 4. If we know Ӯ = 439, then what must 4 be? A. 91 B. 84 C. 90 D. 85 29. Two dice are rolled. What is the probability their sum is a composite number? A. 5/12 B. 1/2 C. 7/12 D. 2/3 30. Suppose a coin is loaded so that it lands heads with probability 0.6. If the coin is flipped 3 times, what is the mean and standard deviation of the number of heads that turn up? (To four decimal places.) A. µ = 1.8; σ = 0.8485 B. µ = 1.8; σ = 0.7265 C. µ = 2; σ = 0.8485 D. µ = 2; σ = 0.7265 6