AP Statistics Semester I Examination Section I Questions 1-30 Spend approximately 60 minutes on this part of the exam.

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1 AP Statistics Semester I Examination Section I Questions 1-30 Spend approximately 60 minutes on this part of the exam. Name: Directions: The questions or incomplete statements below are each followed by five possible answers or completions. Select the choice that best answers the question or completes the statement. 1. The statement The median of a distribution is approximately equal to the mean of the distribution can be made true by adding which of the following: a. for all distributions b. only for symmetric, mound-shaped distributions. c. for skewed distributions. d. for symmetric distributions e. None of these 2. A distribution of weekly sales has a mean of $1,250 with a standard deviation of 230. Which of the following can be concluded from this information? a. The distribution is mound-shaped and symmetric. b. A negative z-score would correspond to a value less than $1,250 c. Some weekly sales are negative. d. A z-score tells the number of standard deviations a value is from the median. e. None of these can be concluded. 3. A linear regression model from a study of weight loss and daily exercise was Weight loss = (Time). This indicates which of the following? a. The correlation coefficient is negative. b. If you exercise longer, you will lose more weight. c. You will gain weight if you don t exercise. d. (0, -0.63) is an outlier. e. None of these is indicated. 5. Suppose the least squares regression line of the set {(hours of part-time work per week, GPA)} for 1,000 high school seniors was GPA= (Hours). The average GPA of students who worked 20 hours per week is approximately: a b c. 2.8 d. The value cannot be determined. e. None of the Above. 6. Which of the following will not be a cause of response bias? a. the level of honesty of the respondent b. wording of questions c. appearance of the interviewer d. the method of selection of participants e. All of these could be a cause of response bias. 7. A sample space contains only 5 elements. Which of the following could not be its probability distribution? Assume that the sets of the probabilities correspond to the elements A, B, C, D, and E. a. {0.3, 0, 0.3, 0, 0.4} b. {0.1, 0.2, 0.3, 0.4, 0.1} c. {0.9, 0.05, 0.05, 0, 0} d. {0, 0, 0, 0, 1} e. All of these are valid sets of probabilities. 4. A residual plot of a linear regression provides evidence of a good fit if which of the following statements are true? I. The points are randomly scattered above and below the horizontal axis. II. The distances from the horizontal axis to the III. points are approximately the same. The values of the deviations from the horizontal axis are small. a. I only b. I and II only c. I, II, III d. II only e. II and III only

2 8. Which of the following statements can be inferred from this histogram? a. median = mean b. median < mean c. median > mean d. The data are skewed left. e. None of these statements can be inferred. 9. Which of the following is no true of a normal curve? a. It is centered at 0 and has a standard deviation of 1. b. It is asymptotic to the x-axis. c. There are points of inflection at 1 standard deviation. d. The area under the curve equals 1. e. All of these are true. 10. Which best describes statistical bias? a. Bias is the tendency for a distribution to be skewed b. Bias is not an issue with symmetric mound-shaped distributions c. Bias increases variation in responses. d. Bias is a systematic error in the survey results. e. None of these describes bias. 11. Which of the following is false about the standard deviation? a. For mound-shaped, symmetric distributions, approximately 95% of the data are within 2 standard deviations of the mean. b. Standard deviation cannot be computed for skewed distributions. c. Standard deviation is the square root of variance. d. For mound-shaped, symmetric distributions, the interval [-1 standard deviation, +1 standard deviation] is wider than the interquartile range. e. All of these are true. 12. A girl scores a 23 in math on the ACT and 560 on the math section of the SAT. Suppose both distributions are approximately normal and the mean of the ACT was 19 with a standard deviation of 6, while the mean of the SAT was 490 with a standard deviation of 140. Which of the following is no true? a. Comparison of z-scores will identify the better score. b. The number of students who took each exam this year compared to past years will impact the comparison of scores. c. The z-score of the ACT score is 0.67 while the z- score of the SAT is 0.5. d. Comparison of percentile will identify the better score. e. All of these are true. 13. At a particular value, the residual for a linear regression has a value of 1.2. Which of the following is a true statement? a. r for the regression. b. The regression line overestimates the actual value of the point. c. The regression line underestimates the actual value of the point. d. A non-linear regression would provide a better fit. e. None of these are true. 14. Randomization a. is necessary in all experimental designs. b. is not required in block design c. is not required in match-pairs designs. d. is for simple random samples. e. reduces the error in the estimate of the mean 15. Which of the following is not a consideration in determining the goodness of fit of a model? r 2 a. the value of b. the slope of its residual plot c. the existence of influential points d. the existence of pattern in the residual points e. All of these are considerations. 16. Subjects for a study of identical twins, one of who has died of cancer, were identified by a nationwide search of hospital records. Once identified, individuals were asked to participate in the study dealing with the effects of the loss on the surviving twin. This method of selection is best described as: a. multi-staged block design b. an observational study c. a randomized experiment d. a voluntary response sample e. a controlled experiment

3 17. A probability distribution of earnings from a $1,000 investment in an Internet company for a term of 3 years is: -$1,000 $0 $1,000 $2,000 $3, How much should you expect to earn from this 3-year investment? a. $800 b. $1,000 c. $1,200 d. $2,000 e. $2, Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint, then the probability that both events occur is: a. 0.0 b. 0.1 c. 0.2 d. 0.9 e. None of the above. 19. Which of the following is not a requirement of a controlled experiment? a. Control b. Comparison c. Replication d. Randomization e. All of these are required. 20. Give the correct order of the following from the least to the greatest in a normal curve. I. 3 rd quartile II. value of the 70 th percentile III. value of a z-score of 1. a. I, II, III b. II, I, III c. III, II, I d. I, III, II e. III, I, II 21. Which of the following is a valid probability density function on the interval [0,2]? a. f x 0. 5x b. f x x c. f x 2x d. f x x e. None of these 22. Which of the following statements are true about discrete probability distributions? I. The sum of the probabilities must equal 1. II. There are a finite number of outcomes. III. All the probabilities must be non-negative. a. I only b. I and II c. I, II, and III d. I and III e. II only 23. Which of the following is resistant to extreme values? I. Mean II. Median III. Inter-Quartile Range IV. Range a. II, III b. I, II, IV c. II, III, IV d. II only e. All are resistant to extreme values 24. The following table displays the results of a sample of 99 subjects in which each person indicated his or her favorite sport of three listed. The data are organized by favorite sport and age group. Age Football Baseball Soccer Over B/t 20 and Under What is the probability that a person chosen at random will be under 20 and favor baseball? a. b. c. d e. None of these 25. A pretzel company calculated that there is a mean of 72.5 broken pretzels in each production run with a standard deviation of 7.1. If the distribution is approximately normal, find the probability that there will be fewer than 60 broken pretzels in a run? a. 0 b c d e. None of these.

4 26. If representation of all four classes in a high school is of importance, which of the following sampling designs is appropriate? a. Simple Random Sample b. Systematic Sample c. Quota Sample d. Stratified Random Sample e. None of these. 27. Which observation has the higher z-score? I. x 25.4; x 12.9; s 3. 7 II. x 137.5; x 73.7; s a. I b. II c. z-scores are equal d. cannot be determined with given information e. None of the above. 28. In a particular game of solitaire, the object of the game is to reduce the card into one stack by moving stacks one to the left or three to the left. Stacks of cards are moved to the left if their top card either matches the suit or the number of the top card of a stack in the position listed above. The following outcomes and probabilities are given: # of stacks Win/Lose $1 $0.50 $0.25 $0 -$0.25 Probability If you were to play this game 10 times, your net winnings should be approximately: a. $0.48 b. $0.12 c. $0.43 d. $0.74 e. None of the above. 29. Given that P(A)=0.125, P(B)=0.237, P(A and B)=0.077, and P(A or B)=0.285, which of the following statements are true? a. A and B are independent and disjoint. b. A and B are independent but not disjoint. c. A and B are disjoint but not independent d. A and B are neither disjoint nor independent e. A and B are joint, but there is not enough information to determine if they are independent. 30. I toss a fair coin a large number of times. Assuming tosses are independent, which of the following is true? a. Once the number of flips is large enough (usually about 10,000) the number of heads will always be exactly half of the total number of tosses. For example, after 10,000 tosses I should have 5,000 heads. b. The proportion of heads will be about 1 2 and this proportion will tend to get closer and closer to 1 2 as the number of tosses increases. c. As the number of tosses increases, any long run of heads will be balanced by a corresponding run of tails so that the overall proportion of heads is 1 2. d. All of the above e. None of the above End of Section I Continue onto Section II: Free-Response Questions

5 Semester I Exam Section II Questions 1-4 Spend about 60 minutes on this section of the exam. Directions: In order to receive full credit for your free-response questions, you must completely analyze each situation and clearly communicate your analyses and results. In order to earn partial credit when warranted, be sure to show enough work so that your reasoning process can be followed. Use the blank paper for your answers. 1. A fast food restaurant chain is conducting an incentive program of including 1 of 6 different characters from a popular cartoon movie ( El Kid, Lo Mejor ) in their children s meal at no extra charge. Each character has the same likelihood of being present in a given children s meal. a. Describe how you would design a simulation using a random digits table to determine the probability that a person will get at least 3 of the 6 characters in a random purchase of 10 children s meals. b. Conduct your simulation three times using a random digits table. Indicate each simulation in a separate row of the table; begin at the far left of each row. Report your findings c. One of the characters is of a new superstar, El Magnifico. Describe how you would design a simulation using a random digits table to determine the probability that a person will get El Magnifico s character before getting El Magnifico s arch rival, Diablito. d. Conduct your simulation three times using the random digits table below. Indicate each simulation in a separate row of the table; begin at the far left of each row The following data are for intelligence-test (IT) scores, grade-point-averages (GPA), and reading rates (RR) of 20 atrisk students. IT GPA RR IT GPA RR a. Calculate the line of best fit that predicts GPA on the basis of IT scores. b. Calculate the line of best fit that predicts GPA on the basis of RR scores. c. Which of the two line calculated in parts a and b best fits the data? Justify your answer citing statistical evidence of goodness of fit.

6 3. A simple random sample of 50 adults who live in a large urban area were asked to indicate the number of parking tickets that each had received over the last 5 years. A stem and leaf plot of the data is shown below Leaf Unit = 1.0, n = 50 a. Draw and label a sketch of the box plot of these data. b. Compare (and contrast) the box to the stem-and-leaf plot. Explain your answer. c. Based on the given stem-and-leaf plot and the box plot you sketched in part a., describe the relation between the mean and the median of these data. 4. An insurance company that specializes in renter s coverage anticipates that it will have to pay benefits to its customers in the amounts listed in the table below. In addition, it estimates the probabilities of each payment: Benefit ($) 500 1,000 2,000 5,000 10,000 Probability a. Does this table specify a probability distribution? Explain the reasons for your answer. b. How much would you estimate that the company can expect to pay for a claim? c. What is the standard deviation of the estimate in part b?