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AP STATISTICS EXAM REVIEW by DAVID CUSTER (click on topic of choice)

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  1. 0 AP STATISTICSEXAM REVIEWby DAVID CUSTER(click on topic of choice) TOPIC II: Experimental Design (15 questions) TOPIC I: Describing Data (15 questions) TOPIC III: Probability (18 questions) TOPIC IV: Inference (15 questions)

  2. 0 TOPIC I: Describing Data • Univariate Data • Normal Distributions • Bivariate Data START TOPIC

  3. 0 Which observation has the higher z-score?I. x=25.4; μ =12.9; σ=3.7II. x=25.4; μ=15.3; σ=2.7 I.1. • I • II • z-scores are equal • cannot be determined since we don’t know the standard deviations of the populations • cannot be determined since we don’t know if the populations are normal Topic I Menu

  4. SOLUTION 0 Which observation has the higher z-score? I. x=25.4; μ =12.9; σ=3.7II. x=25.4; μ=15.3; σ=2.7 I.1. • I • II • z-scores are equal • cannot be determined since we don’t know the standard deviations of the populations • cannot be determined since we don’t know if the populations are normal The z-score for I is 3.38; the z-score for II is 3.74 Topic I Menu

  5. 0 The Quartile and Percentile positions of the value 10 in the set {10, 6, 8, 9, 12, 17, 32, 16}are: I.2. • Q3; 38 • Q2; 38 • Q2; 26 • Q3; 26 • none of these Topic I Menu

  6. SOLUTION 0 The Quartile and Percentile positions of the value 10 in the set {10, 6, 8, 9, 12, 17, 32, 16}are: I.2. • Q3; 38 • Q2; 38 • Q2; 26 • Q3; 26 • none of these When the values are in order, there are 3 values below 10. This puts 10 in the 37.5 percentile and the 2nd quartile. Topic I Menu

  7. 0 The Standard Deviation of the set {5, 7, 7, 8, 10, 11} is 2. Which of the following sets also has a Standard Deviation of 2? I.3. • {4, 5, 8, 12, 14} • {2, 4, 6, 8, 10, 12} • {3, 5, 5, 6, 8, 9} • {10, 14, 14, 16, 20, 22} • none of the above Topic I Menu

  8. SOLUTION 0 The Standard Deviation of the set {5, 7, 7, 8, 10, 11} is 2. Which of the following sets also has a Standard Deviation of 2? I.3. • {4, 5, 8, 12, 14} • {2, 4, 6, 8, 10, 12} • {3, 5, 5, 6, 8, 9} • {10, 14, 14, 16, 20, 22} • none of the above There is a uniform decrease of 2 units in this set. The st. deviation must be the same. Topic I Menu

  9. 0 If 12% of the values of a data set lie between a and b and d is added to each value, then which of the following is true? I.4. • 12% still lies between a and b • 12% lies between a + d and b + d • (12+d)% lies between a and b • (12+d)% lies between a + d and b + d • there is no way to tell how much data is between a and b Topic I Menu

  10. SOLUTION 0 If 12% of the values of a data set lie between a and b and d is added to each value, then which of the following is true? I.4. • 12% still lies between a and b • 12% lies between a + d and b + d • (12+d)% lies between a and b • (12+d)% lies between a + d and b + d • there is no way to tell how much data is between a and b A uniform shift of all the data maintains the percentages of data in shifted intervals. Topic I Menu

  11. If a distribution is relatively symmetric and mount-shaped, order the following (from least to greatest) 1. a z-score of 1 2. the value of Q3 3. a value in the 70th percentile I.5. • 1, 2, 3 • 1, 3, 2 • 3, 2, 1 • 3, 1, 2 • 2, 3, 1 Topic I Menu

  12. SOLUTION 0 If a distribution is relatively symmetric and mount-shaped, order the following (from least to greatest) 1. a z-score of 1 2. the value of Q3 3. a value in the 70th percentile I.5. • 1, 2, 3 • 1, 3, 2 • 3, 2, 1 • 3, 1, 2 • 2, 3, 1 The percentile of a z-score of 1 is about 84%, and the percentile of Q3 is 75% Topic I Menu

  13. 0 Which of the following would NOT be a correct interpretation of a correlation coefficient of r = -.30 I.6. • The variables are inversely related • The coefficient of determination is 0.09 • 30% of the variation between the variables is linear • There exists a weak relationship between the variables • All are correct Topic I Menu

  14. SOLUTION 0 Which of the following would NOT be a correct interpretation of a correlation coefficient of r = -.30 I.6. • The variables are inversely related • The coefficient of determination is 0.09 • 30% of the variation between the variables is linear • There exists a weak relationship between the variables • All are correct The value of r2 explains the variation between the variables. Not r. Topic I Menu

  15. 0 Which of the following displays is best suited for categorical data? I.7. • Box Plot • Bar Graph • Stem and Leaf Plot • Dot Plot • Scatterplot Topic I Menu

  16. SOLUTION 0 Which of the following displays is best suited for categorical data? I.7. • Box Plot • Bar Graph • Stem and Leaf Plot • Dot Plot • Scatterplot In a bar graph, each column is separate, allowing for categorical separation. Topic I Menu

  17. 0 Linear regression usually employs the method of least squares. Which of the following is the quantity that is minimized by the least squares process? I.8. Topic I Menu

  18. SOLUTION 0 Linear regression usually employs the method of least squares. Which of the following is the quantity that is minimized by the least squares process? I.8. Least Squares Regression minimizes the residuals in the y-direction. Topic I Menu

  19. 0 Which of the following is NOT true? I.9. • Two sets of data can have the same means but different variances • Two sets of data can have the same variance but different means • Two different values in a data set can have the same z-score • All the absolute values of z-scores for a data set can be equal • All of the above are true Topic I Menu

  20. SOLUTION 0 Which of the following is NOT true? I.9. Since each value is a distinct distance from the mean, the z-scores must all be different • Two sets of data can have the same means but different variances • Two sets of data can have the same variance but different means • Two different values in a data set can have the same z-score • All the absolute values of z-scores for a data set can be equal • All of the above are true Topic I Menu

  21. 0 In a symmetric, mount-shaped distribution, what percentile has a z-score of -2? I.10. Topic I Menu

  22. SOLUTION 0 In a symmetric, mount-shaped distribution, what percentile has a z-score of -2? I.10. 2.5th percentile We should be able to approximate this with the normal distribution. Area to the left of -2? On the TI-83: Normalcdf(-1E99, -2) = .02275 Topic I Menu

  23. 0 Lee’s z-score on his math test was 1.5. The class average was a 62.1 and the variance was 6.76. What was Lee’s actual grade on the test? I.11. • 60 • 62 • 64 • 66 • 68 Topic I Menu

  24. SOLUTION 0 Lee’s z-score on his math test was 1.5. The class average was a 62.1 and the variance was 6.76. What was Lee’s actual grade on the test? I.11. • 60 • 62 • 64 • 66 • 68 We need to solve the following equation for x: so x=66 Topic I Menu

  25. 0 Does the following problem have a unique solution? If so, find it. If not, show at least two answers:5 numbers have Q1=12, Median=15, Q3=18. Find the mean. I.12. Topic I Menu

  26. SOLUTION 0 Does the following problem have a unique solution? If so, find it. If not, show at least two answers:5 numbers have Q1=12, Median=15, Q3=18. Find the mean. I.12. {11, 13, 15, 17, 19} μ=15 { 9, 15, 15, 17, 19} μ=15 the data sets are not unique, but the mean is always 15! YES!!! surprisingly! Topic I Menu

  27. 0 The average grade on a math test given to two sections is 60.98. Section I has 27 students with a mean grade of 57.30. If the mean grade of Section 2 is 65.30, how many students are in section 2? I.13. Topic I Menu

  28. SOLUTION 0 The average grade on a math test given to two sections is 60.98. Section I has 27 students with a mean grade of 57.30. If the mean grade of Section 2 is 65.30, how many students are in section 2? I.13. 23 students. we arrive at n=23 Topic I Menu

  29. 0 If the mean of 75 values is 52.6 and the mean of 25 values is 48.4; find the mean of all 100 values. I.14. • 51.55 • 52.76 • 56.55 • 56.88 • 59.12 Topic I Menu

  30. SOLUTION 0 If the mean of 75 values is 52.6 and the mean of 25 values is 48.4; find the mean of all 100 values. I.14. • 51.55 • 52.76 • 56.55 • 56.88 • 59.12 75(52.6) + 25(48.4) 100 Topic I Menu

  31. 0 In skewed-right distributions, what is most frequently the relationship of the mean, median, and mode? I.15. • mean > median > mode • median > mean > mode • mode > median > mean • mode > mean > median • mean > mode > median Topic I Menu

  32. SOLUTION 0 In skewed-right distributions, what is most frequently the relationship of the mean, median, and mode? I.15. • mean > median > mode • median > mean > mode • mode > median > mean • mode > mean > median • mean > mode > median The median is resistant, the mean, not at all. So a right skewed distribution will have a mean much higher than median, much higher than mode. Topic I Menu

  33. 0 TOPIC II: Experimental Design • Sampling • Designing Experiments • Observational Studies START TOPIC

  34. A personnel director studied the eating habits of employees by watching a group of employees at lunch. He wishes to see who buys in the cafeteria, who brings a home lunch, and who goes out.The study is categorized as: II.1. • a census • a survey sample • an observational study • a designed experiment • none of these Topic II Menu

  35. SOLUTION A personnel director studied the eating habits of employees by watching a group of employees at lunch. He wishes to see who buys in the cafeteria, who brings a home lunch, and who goes out.The study is categorized as: II.1. • a census • a survey sample • an observational study • a designed experiment • none of these The director is observing behavior, not implementing treatments on the group Topic II Menu

  36. A personnel director studied the eating habits of employees by watching a group of employees at lunch. He wishes to see who buys in the cafeteria, who brings a home lunch, and who goes out.If the director only looks at those in one department, she is performing: II.2. • a simple random sample • a quota sample • a convenience sample • a multi-stage cluster sample • a census Topic II Menu

  37. SOLUTION A personnel director studied the eating habits of employees by watching a group of employees at lunch. He wishes to see who buys in the cafeteria, who brings a home lunch, and who goes out.If the director only looks at those in one department, she is performing: II.2. • a simple random sample • a quota sample • a convenience sample • a multi-stage cluster sample • a census Without a properly randomized selection, she is introducing bias to the study. Topic II Menu

  38. A personnel director studied the eating habits of employees by watching a group of employees at lunch. He wishes to see who buys in the cafeteria, who brings a home lunch, and who goes out.If the director selects 50 employees at random and categorizes by gender, she is: II.3. • blocking for gender • testing for a lurking variable • promoting sexual harassment • testing for bias • none of these Topic II Menu

  39. SOLUTION A personnel director studied the eating habits of employees by watching a group of employees at lunch. He wishes to see who buys in the cafeteria, who brings a home lunch, and who goes out.If the director selects 50 employees at random and categorizes by gender, she is: II.3. • blocking for gender • testing for a lurking variable • promoting sexual harassment • testing for bias • none of these She is investigating whether gender affects lunchtime behavior Topic II Menu

  40. Which of the following is NOT a concern in data collection? II.4. • lurking variables • blocking • bias • non-response • all of the above are concerns Topic II Menu

  41. SOLUTION Which of the following is NOT a concern in data collection? II.4. • lurking variables • blocking • bias • non-response • all of the above are concerns Even blocking methods need to be analyzed Topic II Menu

  42. Which of the following is NOT a valid sample design? II. 5. • Code every member of a population and select 100 randomly chosen members • Divide a population by gender and select 50 individuals randomly from each group • Select individuals randomly and place into gender groups until you have the same proportion as in the population • Select five homerooms at random from all the homerooms in a large high school. • All of these are valid Topic II Menu

  43. SOLUTION Which of the following is NOT a valid sample design? II. 5. • Code every member of a population and select 100 randomly chosen members • Divide a population by gender and select 50 individuals randomly from each group • Select individuals randomly and place into gender groups until you have the same proportion as in the population • Select five homerooms at random from all the homerooms in a large high school. • All of these are valid But you may be able to question the validity of answer (C) Topic II Menu

  44. An insurance company conducted a study to determine the percent of cardiologists who had been sued over the last 5 yrs.The variable of interest is: II.6. • the doctor’s specialty, e.g. cardiology, obstetrics, etc. • the number of doctors who are cardiologists • all cardiologists in the American Medical Association directory • a random sample of 100 cardiologists • none of these Topic II Menu

  45. SOLUTION An insurance company conducted a study to determine the percent of cardiologists who had been sued over the last 5 yrs.The variable of interest is: II.6. • the doctor’s specialty, e.g. cardiology, obstetrics, etc. • the number of doctors who are cardiologists • all cardiologists in the American Medical Association directory • a random sample of 100 cardiologists • none of these we are interested in the percentage of doctors who have been sued Topic II Menu

  46. An insurance company conducted a study to determine the percent of cardiologists who had been sued over the last 5 yrs.The population of interest is: II.7. • the set of all doctors who were sued for malpractice • the set of cardiologists who were sued for malpractice • all doctors • all cardiologists • all doctors who have malpractice insurance Topic II Menu

  47. SOLUTION An insurance company conducted a study to determine the percent of cardiologists who had been sued over the last 5 yrs.The population of interest is: II.7. • the set of all doctors who were sued for malpractice • the set of cardiologists who were sued for malpractice • all doctors • all cardiologists • all doctors who have malpractice insurance Just cardiologists, not all doctors. Topic II Menu

  48. An insurance company conducted a study to determine the percent of cardiologists who had been sued over the last 5 yrs.Which could be used to gather the data? II.8. • a designed experiment • a census of all cardiologists • an observational study of randomly selected cardiologists • a survey sent to randomly selected cardiologists • any answer except (A) Topic II Menu

  49. SOLUTION An insurance company conducted a study to determine the percent of cardiologists who had been sued over the last 5 yrs.Which could be used to gather the data? II.8. • a designed experiment • a census of all cardiologists • an observational study of randomly selected cardiologists • a survey sent to randomly selected cardiologists • any answer except (A) This population of this observational study is too large to track everyone down. Topic II Menu

  50. Which of the following is NOT a source of bias in sample surveys? II.9. • non-response • wording of questions • voluntary response • use of a telephone survey • all are sources of bias Topic II Menu