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JEOPARDY!

JEOPARDY!. Click Once to Begin. FULL YEAR AP STATISTICS REVIEW. JEOPARDY!. I, II, III… GO!. PRO BA BIL ITY!. Keenan ’ s TOP PICKS. INFER ENCE. 2002 AP EXAM. Let ’ s Get A 5!. 100. 100. 100. 100. 100. 100. 200. 200. 200. 200. 200. 200. 300. 300. 300. 300. 300. 300. 400.

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JEOPARDY!

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  1. JEOPARDY! Click Once to Begin FULL YEAR AP STATISTICS REVIEW

  2. JEOPARDY! I, II, III… GO! PRO BA BIL ITY! Keenan’s TOP PICKS INFER ENCE. 2002 AP EXAM Let’s Get A 5! 100 100 100 100 100 100 200 200 200 200 200 200 300 300 300 300 300 300 400 400 400 400 400 400 500 500 500 500 500 500

  3. INFERENCE 74Which of the following are true?I. The power of a test concerns it’s ability to correctly reject a false Null Hypothesis.II. The significance level of a test is the probability of rejecting a true Null Hypothesis.III. The probability of a Type I error plus the probability of a Type II error is always equal to 1.(A) I and II(B) I and III(C) II and III(D) I, II, and III(E) None are true.

  4. (A) I and II. I is the definition of power, II is a Type I error, or alpha. III is false.

  5. EXPERIMENTAL DESIGN 29Which of the following are true statements about sampling?I. Careful analysis of a given sample will indicate whether or not it is random.II. Sampling error implies an error, possibly very small, but still an error, on the part of the surveyor.III. Data obtained when conducting a census are always more accurate than data obtained from a sample, no matter how careful the design of the sample study.(A) I only(B) II only(C) III only(D) None of the statements are true(E) None of the above gives the complete set of true responses

  6. (D) To determine if a sample is random, one must analyze the procedure by which it was obtained. Sampling error is natural variation, not an actual error. If a census is poorly run, it will actually provide less accurate information than a well-designed survey. For example, having the principal ask every single student whether or not he or she regularly cheats on exams produces less useful data than a carefully worded anonymous questionnaire filled out by a randomly selected sample of the student body.

  7. INFERENCE 89If all other variables remain constant, which of the following will increase the power of a hypothesis test?I. Increasing the sample sizeII. Increasing the significance levelIII. Increasing the probability of a Type II error(A) I only(B) II only(C) III only(D) I and II(E) All are true

  8. (D) I and IIIncreasing the sample size WILL increase power. Increasing the significance level is the same as increasing alpha (Type I error) which also increases power. Increasing the probability of a Type II error will actually decrease power.

  9. EXPERIMENTAL DESIGN 35Consider the following three events:I. Although 75% of Cubs fans believe they will go to the World Series this year, in a random sample of 50 Cubs fans, only 30 “believe”II. In a survey about literacy, an embarrassed adult deliberately liesIII. A surveyor mistakenly records answers to one question in the wrong space.Which of the following correctly characterizes the above?(A) I – sampling error, II – response bias, III – human mistake(B) I – sampling error, II – nonresponse bias, III – hidden error(C) I – hidden bias, II – voluntary bias, III – sampling error(D) I – undercoverage error, II – voluntary error, III – unintentional error(E) I – small sample, II – deliberate error, III – mistaken error

  10. (A) I – sampling error, II – response bias, III – human mistake

  11. DATA ANALYSIS 75Which of the following are true statements?I. If a sample has variance zero, the variance of the population is also zero.II. If the population has variance zero, the variance of the sample is also zero.III. If the sample has variance zero, the sample mean and the sample median are equal.(A) I and II(B) I and III(C) II and III(D) I, II, and III(E) None of the above gives the complete set of true responses.

  12. (C) II and III If the variance of a set is zero, all the values in the set are equal. If all the values in the population are equal, the same holds true for any sample of that population. However, if all the values of a sample are the same, that doesn’t necessarily hold true for the whole population. If all the values in a set are equal, then the mean and the median both equal this common value and thus equal each other.

  13. PROBABILITY 46Suppose 56 percent of 8 to 12 year olds expect to have a “great life.” In an SRS of 125 eight to twelve year olds, what is the probability that between 50 percent and 60 percent will say they expect to have a “great life”?(A) .2721(B) .5402(C) .6723(D) .7279(E) .8640

  14. (D) .7279The sampling distribution of p-hat has mean .56 and standard deviation [sqrt(pq/n)] = .0444. The probability that lies between .50 and .60 is .7279

  15. PROBABILITY 63For which of the following is a binomial an appropriate model?(A) The number of heads in ten tosses of an unfair coin weighted so that heads comes up twice as often as tails.(B) The number of hits in five at-bats where the probability of a hit is either .352 or .324 depending upon whether the pitcher is left or right-handed(C) The number of tosses of a fair coin before heads appears on two consecutive tosses.(D) The number of snowy days in a given week.(E) The binomial is appropriate in all of the above.

  16. (A) In choice B, p is not constant. In choice C, they’re asking about the first success (two heads in a row). In choice D, it is not safe to assume independence of a snow day from one day to the next.

  17. PROBABILITY 32Given the probabilities Pr(A) = .3 and Pr(A or B) = .7, what is the probability Pr(B) if A and B are mutually exclusive? If A and B are independent?(A) .4, .3(B) .4, 4/7(C) 4/7, .4(D) .7, 4/7(E) .7, .3

  18. (B) If A and B are mutually exclusive, then Pr(A) + Pr(B) = Pr(A or B), thus Pr(B) = .4If A and B are independent, then Pr(A and B) = Pr(A)Pr(B). Thus, by the General Addition Rule, Pr(A or B) = Pr(A) + Pr(B) – Pr(A and B) or .7 = .3 + Pr(B) - .3Pr(B) yielding Pr(B) = 4/7

  19. PROBABILITY 39The Air Force receives 40 percent of its parachutes from company C1 and the rest from company C2. The probability that a parachute will fail to open is .0025 or .002, depending on whether it is from company C1 or C2, respectively. If a randomly chosen parachute fails to open, what is the probability that it is from company C1?(A) .0010(B) .0022(C) .4025(D) .4545(E) .5455

  20. (D) .4545Create a tree diagram, set up a conditional probability. Pr(C1|fails) = Pr(BOTH) / Pr(fails)

  21. PROBABILITY 64In a set of eight boxes, three boxes each contain two red and two green marbles, while the remaining boxes each contain three red and two green marbles. A player randomly picks a box and then randomly picks a marble from that box. She wins if she ends up with a red marble. If she plays four times, what is the probability she wins exactly twice?(A) .0606(B) .3164(C) .3221(D) .3634(E) .5625

  22. (D) .3634The probability of winning is (3/8 x ½) + (5/8 x 3/5) = 9/16, and the probability of winning exactly twice in 4 games is found using the binomial model for 2 successes in 4 trials, with a probability of success at 9/16.

  23. INFERENCE 3In general, how does doubling the sample size change the confidence interval size?(A) Doubles the interval size(B) Halves the interval size(C) Multiplies the interval size by 1.414(D) Divides the interval size by 1.414(E) The question cannot be answered without knowing the sample size

  24. (D) Increasing the sample size by a multiple of d divides the interval by sqrt(d)

  25. PROBABILITY 58The number of hybrid cars a dealer sells weekly has the following probability distribution:The dealer purchases the cars for $21,000 and sells them for $24,500. What is the expected weekly profit from selling hybrid cars?(A) $2,380(B) $3,500(C) $5,355(D) $8,109(E) $ 37,485

  26. (C) $5,355The expected number of cars sold per week is 1.53. Profit = 1.53($3,500) = $5, 355

  27. INFERENCE 69A manufacturer of heart-lung machines periodically checks a sample of its product and performs a major recalibration if readings are sufficiently off target. Similarly, a rug factory periodically checks the sizes of its throw rugs coming off an assembly line and halts production if measurements are sufficiently off target. In both situations, we have the null hypothesis that the equipment is performing satisfactorily. For each situation, which is the more serious concern?(A) Machine producer: Type I error, carpet manufacturer: Type I error(B) Machine producer: Type I error, carpet manufacturer: Type II error(C) Machine producer: Type II error, carpet manufacturer: Type I error(D) Machine producer: Type II error, carpet manufacturer: Type II error(E) There is insufficient information to answer this question

  28. (C) In the production of heart-lung machines, the more serious concern would be a Type II error, which is that the equipment is not performing correctly, but the check does not pick this up. As for the rugs, the more serious concern would be a Type I error, which is that the equipment is performing just fine, but the check causes them to halt production.

  29. PROBABILITY 29Suppose Pr(X) = .25 and Pr(Y) = .40. If Pr(X|Y) = .20, what is Pr(Y|X)?(A) .10(B) .125(C) .32(D) .45(E) .50

  30. (C) Pr(X and Y) = Pr(Y)Pr(X|Y) = (.20)(.40) = .08.Then Pr(Y|X) = Pr(X and Y) / Pr(X) = .08/.25 = .32

  31. PROBABILITY 62Following are parts of the probability distributions for the random variables X and Y.If X and Y are independent and the joint probability Pr(X = 1, Y = 2) = .1, what is Pr(X = 4)?(A) .1(B) .2(C) .3(D) .4(E) .5

  32. (C) Pr(Y=2) = .5By independence, Pr(X=1, Y=2) = Pr(X=1)Pr(Y=2), and so .1 = Pr(X=1)(.5) and Pr(X=1) = .2. Then Pr(X=4) = .3

  33. INFERENCE 82A high school has six math teachers and six science teachers. When comparing their mean years of service, which of the following is most appropriate?(A) A two-sample z-test of population means(B) A two-sample t-test of population means(C) A one-sample z-test for means(D) A one-sample t-test for means(E) None of the above are appropriate

  34. (E) With a population of 12, we will run no such tests. CENSUS!

  35. INFERENCE 30A congressional representative serving on the Joint Committee on Taxation states that the average yearly charitable contributions for taxpayers is $1,250. A lobbyist for a national church organizations who believes that the real figure is lower samples 12 families and comes up with a mean of $1,092 and a standard deviation of $308. Where is the p-value?(A) Below .01(B) Between .01 and .025(C) Between .025 and .05(D) Between .05 and .10(E) Over .10

  36. (D) This is a left-tailed test with a t-score of -1.777 and a p-value of .0516.

  37. INFERENCE 64Which of the following are true statements?I. The significance level of a test is the probability of a Type II error.II. Given a particular alternative, the power of a test against that alternative is 1 minus the probability of the Type II error associated with that alternative.III. If the significance level remains fixed, increasing the sample size will reduce the probability of a Type II error.(A) II only(B) III only(C) I and II(D) I and III(E) II and III

  38. (E) The significance level is the probability of a Type I, not a Type II error.

  39. INFERENCE 62There are 50,000 high school students in an extended metropolitan region. As each of their students came in to register for classes, guidance counselors were instructed to use a calculator to pick a random number between 1 and 100. If the number 50 was picked, the student was included in the survey. For one of the may surveys, 30% of the students said they couldn’t live without instant messaging. Are all conditions met for constructing a confidence interval of the true proportion of this region’s teens who believe they cannot live without instant messaging?(A) No, there is no guarantee that a representative random sample is chosen.(B) No, the sample size is not less than 10% of the population.(C) No, np and nq are not both greater than 10.(D) No, there is no reason to assume the population has a normal distribution.(E) Yes, all conditions are met, and a confidence interval can be constructed.

  40. (E) Sample is random, and there is no reason to believe it is not representative. Approximately 1 out of every 100 students will be chosen and 1% is clearly < 10% of the population. Np = 150 and nq = 350 are both greater than 10. Nearly normal is a condition for means, not proportions.

  41. INFERENCE 111Changing from a 95% confidence interval estimate for a population proportion to a 99% confidence interval estimate, with all other things being equal,(A) Increases the interval size by 4 percent.(B) Decreases the interval size by 4 percent.(C) Increases the interval size by 31 percent(D) Decreases the interval size by 31 percent.(E) This question cannot be answered without knowing the sample size.

  42. (C) The critical z will go from 1.96 to 2.576, resulting in an increase in the interval size: 2.576/1.96 = 1.31, or an increase of 31 percent.

  43. Suppose that 30 percent of the subscribers to a cable television service watch the shopping channel at least once a week. You are to design a simulation to estimate the probability that none of five randomly selected subscribers watches the shopping channel at least once a week. Which of the following assignments of the digits 0 through 9 would be appropriate for modeling an individual subscriber's behavior in this simulation? (A) Assign "0, 1, 2" as watching the shopping channel at least once a week and "3, 4, 5, 6, 7, 8, and 9" as not watching, (B) Assign "0, 1, 2, 3" as watching the shopping channel at least once a week and "4, 5, 6, 7, 8, and 9" as not watching. (C) Assign "1, 2, 3, 4, 5" as watching the shopping channel at least once a week and "6, 7 , 8, 9, and 0" as not watching. (D) Assign "0" as watching the shopping channel at least once a week and "1, 2, 3, 4, and 5" as not watching; ignore digits "6, 7, 8, and 9," (E) Assign "3" as watching the shopping channel at least once a week and "0, 1, 2, 4, 5, 6, 7, 8, and 9" as not watching.

  44. (A)

  45. Which of the following statements is (are) true about the t-distribution with k degrees of freedom? I. The t-distribution is symmetric. II. The t-distribution with k degrees of freedom has a smaller variance than the t-distribution with k + 1 degrees of freedom. III. The t-distribution has a larger variance than the standard normal (z) distribution.(A) I only(B) II only(C) III only(D) I and II(E) I and III

  46. (E) I and III

  47. As lab partners, Sally and Betty collected data for a significance test. Both calculated the same z-test statistic, but Sally found the results were significant at the alpha = 0.05 level while Betty found that the results were not. When checking their results, the women found that the only difference in their work was that Sally used a two-sided test, while Betty used a one-sided test. Which of the following could have been their test statistic?(A) -1.990(B) -1.690(C) 1.340(D) 1.250(E) 1.640

  48. (B) -1.690

  49. Suppose that the distribution of a set of scores has a mean of 47 and a standard deviation of 14. If 4 is added to each score, what will be the mean and the standard deviation of the distribution of new scores? MeanStandard Deviation (A) 51 14(B) 51 18(C) 47 14(D) 47 16(E) 47 18

  50. (A)

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