FULL YEAR AP STATISTICS REVIEW

FULL YEAR AP STATISTICS REVIEW
JEOPARDY! Click Once to Begin FULL YEAR AP STATISTICS REVIEW To change the question and answer slides, select the question or answer text box and type in your own questions and answers. To play, click on a question on the game board to go to that question. The house icon will take you to the game board and the question mark icon will take you to the answer slide. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Daily Double Graphic and Sound Effect!
DO NOT DELETE THIS SLIDE! Deleting it may cause the game links to work improperly. This slide is hidden during the game, and WILL not appear. In slide view mode, copy the above (red) graphic (click once to select; right click the border and choose “copy”). Locate the answer slide which you want to be the daily double Right-click and choose “paste”. If necessary, reposition the graphic so that it does not cover the answer text. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

INFERENCE 74 Which of the following are true. I
INFERENCE 74 Which 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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(A) I and II. I is the definition of power, II is a Type I error, or alpha. III is false.
Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

EXPERIMENTAL DESIGN 29 Which 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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

INFERENCE 89 If all other variables remain constant, which of the following will increase the power of a hypothesis test? I. Increasing the sample size II. Increasing the significance level III. 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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(D) I and II Increasing the sample size WILL increase power
(D) I and II Increasing 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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

EXPERIMENTAL DESIGN 35 Consider the following three events: I
EXPERIMENTAL DESIGN 35 Consider 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 lies III. 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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

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

DATA ANALYSIS 75 Which of the following are true statements. I
DATA ANALYSIS 75 Which 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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

PROBABILITY 46 Suppose 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) (B) (C) (D) (E) .8640 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(D). 7279 The sampling distribution of p-hat has mean
(D) The sampling distribution of p-hat has mean .56 and standard deviation [sqrt(pq/n)] = The probability that lies between .50 and .60 is .7279 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

PROBABILITY 63 For 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 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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(A) In choice B, p is not constant
(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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

PROBABILITY 32 Given the probabilities Pr(A) =. 3 and Pr(A or B) =
PROBABILITY 32 Given 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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(B) If A and B are mutually exclusive, then Pr(A) + Pr(B) = Pr(A or B), thus Pr(B) = .4 If 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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

PROBABILITY 39 The 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 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) (B) (C) (D) (E) .5455 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(D). 4545 Create a tree diagram, set up a conditional probability
(D) Create a tree diagram, set up a conditional probability. Pr(C1|fails) = Pr(BOTH) / Pr(fails) Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

PROBABILITY 64 In 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) (B) (C) (D) (E) .5625 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(D) The 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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

INFERENCE 3 In 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 (D) Divides the interval size by (E) The question cannot be answered without knowing the sample size Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

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

# of hybrids 1 2 3 4 5 Pr(X=x) .32 .28 .15 .11 .08 .06 PROBABILITY 58 The 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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(C) $5,355 The expected number of cars sold per week is 1. 53
(C) $5,355 The expected number of cars sold per week is Profit = 1.53($3,500) = $5, 355 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

INFERENCE 69 A 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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

PROBABILITY 29 Suppose Pr(X) =. 25 and Pr(Y) =. 40. If Pr(X|Y) =
PROBABILITY 29 Suppose 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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(C) Pr(X and Y) = Pr(Y)Pr(X|Y) = (. 20)(. 40) =. 08
(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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

X Pr(X) 1 ? 2 .2 3 .3 4 Y Pr(Y) 1 .4 2 ? 3 .1 PROBABILITY 62 Following 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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(C) Pr(Y=2) = .5 By 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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

INFERENCE 82 A 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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

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

INFERENCE 30 A 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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(D) This is a left-tailed test with a t-score of -1
(D) This is a left-tailed test with a t-score of and a p-value of Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

INFERENCE 64 Which of the following are true statements. I
INFERENCE 64 Which 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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

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

INFERENCE 62 There 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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

INFERENCE 111 Changing 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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(C) The critical z will go from 1. 96 to 2
(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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

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. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(A) Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

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 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(E) I and III Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

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) (B) (C) (D) (E) 1.640 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(B) Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Suppose that the distribution of a set of scores has a mean of 47 and a standard deviation of If 4 is added to each score, what will be the mean and the standard deviation of the distribution of new scores? Mean Standard Deviation (A) (B) (C) (D) (E) Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(A) Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

The correlation between two scores X and Y equals 0. 8
The correlation between two scores X and Y equals If both the X scores and the Y scores are converted to z-scores, then the correlation between the z-scores for X and the z-scores for Y would be (A) (B) (C) 0.0 (D) 0.2 (E) 0.8 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(E) .8 Converting to z-scores is a combination of shifting and scaling, neither of which affects the correlation Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

DATA ANALYSIS Consider the points (-1, 4), (2, 10), (4, 15), (7, 21), (10, n). What should n be so that the correlation between the x and y values is r = 1? (A) 26 (B) 27 (C) 28 (D) A value different from any of the above (E) No value for n can make r = 1 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(E) Close observation readily shows that the first four points do not all lie on the same line, and the only way r = 1 is when all of the points lie on the same line. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

EXPERIMENTAL DESIGN 24 Before taking an exam, students either went to bed at their normal times or were sleep deprived for 4 or 8 hours. Half of each group were given a caffeine pill before taking the exam. Determine the number of factors, levels for each, and number of treatments. (A) One factor with two levels, five treatments (B) Two factors, one with one and one with two levels, three treatments (C) Two factors, one with two and one with three levels, five treatments (D) Two factors, one with two and one with three levels, six treatments (E) Three factors, each with two levels, six treatments Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(D) Two factors, sleep deprivation (three levels) and caffeine (two levels), with 3 x 2 = 6 treatments. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

INFERENCE 97 In the following table, what value of n results in a table showing perfect independence? (A) (B) (C) (D) (E) 100 40 60 50 n Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(D) Relative frequencies must be equal throughout
(D) Relative frequencies must be equal throughout. 75 yields this result. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

PROBABILITY 31 The diastolic pressure among 20 to 30 year olds is roughly normal. If 10 percent have levels above 86 mmHg, and 20 percent have levels below 69 mmHg, what is the mean of this distribution? (A) 74.7 mmHg (B) 75.7 mmHg (C) 77.5 mmHg (D) 79.3 mmHg (E) The mean cannot be calculated from the given information Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(B) 75.7 mmHg Create two equations and solve for the mean.

PROBABILITY 74 Suppose X and Y are independent random variables, both with normal distributions. If X has a mean of 30 and a standard deviation of 6, and Y has mean 25 with standard deviation 4, what is the probability that a randomly generated value of X is greater than a randomly generated value of Y? (A) (B) (C) (D) (E) .8413 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

(D) We are looking for the Pr(X>Y) or the Pr(X-Y>0)
(D) We are looking for the Pr(X>Y) or the Pr(X-Y>0). X - Y has mean of 30 – 25 = 5 and standard deviation (through the ADDING of the variances) of Use normcdf to find Pr(X-Y>0) = .7560 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

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