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AP STATISTICS

AP STATISTICS. Fall Semester Review. About the test. 35 questions, all multiple choice Fairly even split among CHAPTERS 1-3 CHAPTERS 5-6. #1.

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AP STATISTICS

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  1. AP STATISTICS Fall Semester Review

  2. About the test 35 questions, all multiple choice Fairly even split among CHAPTERS 1-3 CHAPTERS 5-6

  3. #1 IQs among undergraduates at Mountain Tech are approximately normally distributed. The mean undergraduate IQ is 110. About 95% of undergraduates have IQs between 100 and 120. The standard deviation of these IQs is about A) 25. B) 5. C) 20. D) 15. E) 10.

  4. #2 The least-squares regression line is fit to a set of data. If one of the data points has a positive residual, then A) you have over predicted the response variable. B) you have under predicted the response variable. C) you have under predicted the explanatory variable. D) you have over predicted the explanatory variable. E) you have only predicted positive values.

  5. #3 Suppose we fit the least-squares regression line to a set of data. If a plot of the residuals shows a curved pattern, A) a straight line is not a good summary for the data. B) the correlation must be 0. C) outliers must be present. D) r 2 = 0. E) the correlation must be positive

  6. #4 A quality control inspector on an assembly line making microwave ovens randomly chooses one of the first ten ovens manufactured each day. This oven and every tenth oven thereafter gets inspected. This is called A) a completely randomized design. B) stratified random sampling. C) convenience sampling. D) systematic random sampling. E) simple random sampling.

  7. #5 Light bulbs produced at the Lenin Electrical Works factory in Volgagrad are defective with probability .12. To simulate the event that a single light bulb produced at the Lenin Electrical Works is defective, the CIA could use two digits from a random generator with the convention A) 00, 01, 02, ..., 85, 86, 87 > nondefective 88, 89, 90, ..., 97, 98, 99 > defective B) 00, 01, 02, ..., 09, 10, 11 > defective 12, 13, 14, ..., 97, 98, 99 > nondefective C) 01, 02, 03, ..., 10, 11, 12 > defective 13, 14, 15, ..., 98, 99, 00 > nondefective D) any of the above. E) none of the above.

  8. #6 You want to take an SRS of 50 of the 816 students who live in a dormitory on campus. You label the students 001 to 816 in alphabetical order. In the table of random digits you read the entries 95592 94007 69769 33547 72450 16632 81194 The first three students in your sample have labels A) 400, 769, 769. D) 559, 294, 007. B) 929, 400, 769. E) 955, 929, 400. C) 400, 769, 335.

  9. #7 If the test scores of a class of 30 students have a mean of 75.6 and the test scores of another class of 24 students have a mean of 68.4, then the mean of the combined group is a. 72 b. 72.4 c. 72.8 d. 74.2 e. None of these

  10. #8 A random survey was conducted to determine the cost of residential gas heat. Analysis of the survey results indicated that the mean monthly cost of gas was $125, with a standard deviation of $10. If the distribution is approximately normal, what percent of homes will have a monthly bill of more than $115? a. 34% b. 50% c. 68% d. 84% e. 97.5%

  11. #9 The average life expectancy of males in a particular town is 75 years, with a standard deviation of 5 years. Assuming that the distribution is approximately normal, the approximate 15th percentile in the age distribution is: a. 60 b. 65 c. 70 d. 75 e. 80

  12. #10 • John’s doctor told him that the standardized score (z-score) for • his systolic blood pressure, as compared to the blood pressure of • other men his age, is 2.05. Which of the following is the best • interpretation of this standardized score? • John’s systolic blood pressure is 205. • John’s systolic blood pressure is 2.05 standard deviations above the average systolic blood pressure of men his age. • John’s systolic blood pressure is 2.05 above the average systolic blood pressure of men his age. • John’s systolic blood pressure is 2.05 times the average systolic blood pressure of men his age. • Only 2.05% of men John’s age have a higher systolic blood pressure than he does.

  13. #11 Given a set of ordered pairs (x, y) so that Sx=1.6, Sy=0.75, and r=0.55, what is the slope of the LSRL? a) 1.82 b) 1.17 c) 2.18 d) 0.26 e) 0.78

  14. #12 There is an approximate linear relationship between the height of females and their age (from 5 to 18 years) described by: height = 50.3 + 6.01(age) where height is measured in cm and age in years. Which of the following is not correct? a. The estimated slope is 6.01 which implies that children increase by about 6 cm for each year they grow older. b. The estimated height of a child who is 10 years old is about 110 cm. c. The estimated intercept is 50.3 cm which implies that children reach this height when they are 50.3/6.01=8.4 years old. d. The average height of children when they are 5 years old is about 50% of the average height when they are 18 years old. e. My niece is about 8 years old and is about 115 cm tall. She is taller than average.

  15. #13 A random sample of 35 world-ranked chess players provides hours of study with a mean of 6.2 and standard deviation of 1.3 to winnings with a mean of $208,000 and standard deviation of $42,000. The correlation coefficient is 0.15. Find the equation of the LSRL. a. Winnings = 4850(Hours) + 178,000 b. Winnings = 6300(Hours) + 169,000 c. Winnings = 31,200(Hours) + 14,550 d. Winnings = 32,300(Hours) + 7750 e. Winnings = 42,000(Hours) - 52,400

  16. #14 In a particular rural region, 65% of the residents are smokers, and research indicates that 15% of the smokers have some form of lung cancer. The probability that a resident is a smoker and has lung cancer is • 0.0975 • 0.2308 • 0.15 • 0.65 • 0.0525

  17. #15 Suppose that, in a certain part of the world, in any 50 year period, the probability of a major plague is 0.39, the probability of a major famine is 0.52, and the probability of both a plague and a famine is 0.15. What is the probability of neither a famine nor a plague? • 0.24 • 0.288 • 0.37 • 0.385 • 0.76

  18. #16 The change in scales makes it hard to compare scores on the 1994 math SAT (mean 470, standard deviation 110) and the 1996 math SAT (mean 500, standard deviation 100). Jane took the SAT in 1994 and scored 500. Her sister Colleen took the SAT in 1996 and scored 520. Who did better on the exam, and how can you tell? A) Colleen—she scored 20 points higher than Jane. B) Colleen—her standard score is higher than Jane's. C) Can't tell from the information given. D) Jane—the standard deviation was bigger in 1994. E) Jane—her standard score is higher than Colleen's.

  19. #17 The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded passing grade? A) 57. B) 62. C) 40. D) 44. E) 43.

  20. #18 A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so x helps explain y. The least-squares regression line for predicting y from x is y = 1344 – 19x. On a day when the temperature is 20˚F, the regression line predicts that gas used will be about • 1325 cubic feet • 1724 cubic feet • 964 cubic feet • 1383 cubic feet • None of these

  21. #19 Suppose we fit the least-squares regression line to a set of data. If a plot of the residuals shows a curved pattern, • outliers must be present. • the correlation must be positive. • r2 = 0. • the correlation must be 0. • a straight line is not a good summary for the data.

  22. #20 One hundred volunteers who suffer from severe depression are available for a research study to test the effectiveness of a new drug in treating severe depression. What is the best method to use to test the effectiveness of this new drug against the old drug? • Randomly assign volunteers to two groups: one group will take the new drug and the other group takes the old drug. • Randomly choose volunteers and allow them to select which drug they want to take. • Randomly choose volunteers to take the new drug and ask volunteers using the old drug how effective the old drug is. • Randomly assign volunteers to two groups: one group will take the new drug and the other group takes a placebo. • Assign the new drug to the volunteers who are the most severely depressed and assign the old drug to the least depressed volunteers.

  23. #21 The following text is a computer printout from regression analysis on a program called Data Desk. The data compares the temperature of Bismarck, North Dakota to New York, on randomly selected days. Variable         Coefficient          Constant          23.5915               r2 = 99.0%             Bismarck           0.740767           r2(adj) = 98.9%    Which is the best interpretation of the slope of the regression line? • For each degree increase in Bismarck, the New York temperature increases by 23.5915 degrees. • For each degree increase in New York, the Bismarck temperature increases by 0.740767 degrees. • For each degree increase in Bismarck, the New York temperature increases by 0.740767 degrees. • For each degree increase in New York, the Bismarck temperature increases by 23.5915 degrees. • For each degree increase in New York, the Bismarck temperature increases by .99 degrees.

  24. #22 A forester measured 27 of the trees in a large woods that is up for sale. He found a mean diameter of 10.4 inches and a standard deviation of 4.7 inches. Suppose that these trees provide an accurate description of the whole forest and that a Normal model applies. If a certain tree is at a z = 1.3. What is the diameter of the tree?   • 9.1 inches • 11.7 inches • 16.51 inches • 13.52 inches • 6.11 inches              

  25. #23 You are comparing the results of males and females in an experiment. Which graphical display would you NOT use? • dot plots • Parallel box plots • scatter plot • histogram • Back-to-back stem plots              

  26. #24 The correlation coefficient measures • whether or not a scatter plot shows an interesting pattern. • the strength of the linear relationship between two quantitative variables. • the strength of the relationship between two quantitative variables. • whether there is a relationship between two variables. • whether a cause and effect relation exists between two variables.

  27. #25 If the point in the upper right corner of this scatter plot is removed from the data, what will happen to the slope of the line of best fit and the correlation coefficient? • Both will increase. • Both will decrease. • Slope will increase, r will decrease. • Slope will decrease, r will increase. • Both will remain the same.

  28. #26 To check the effect of heat on durability of crack sealant for Sidewalks, two brands of sealant are used, one brand of economy sealant and one brand of commercial sealant are tested. Twenty tubes from the economy sealant are placed in an extremely high temperature oven for ten hours and twenty tubes from the commercial sealant are placed at room temperature. The amount of leakage is measured on each sealant, and the mean for the economy sealant is compared to the mean for the commercial sealant. Is this a good experimental design? A. No, because the means are not proper statistics for comparison. B. No, because more than two brands should be used. C. No, because more temperatures should be used. D. No, because temperature is confounded with brand. E. Yes

  29. #27 A survey of 57 students was conducted to determine whether or not they held jobs outside of school. Of the 57 students, 31 had no job. Of the Juniors surveyed only 5 had no job. I. Are the events “Junior” and “no job” independent event? II. Are the events “Junior” and “no job” disjoint events? • yes; no • no; no • yes; yes • no; yes • Not enough information is given.

  30. #28 A company wanted to determine the health care costs of its employees. A sample of 50 employees were interviewed and their medical expenses for the previous year were determined. Later the company discovered that the highest medical expense in the sample was mistakenly recorded as 25 times the actual amount. However, after correcting the error, the corrected amount was still greater than or equal to any other medical expense in the sample. Which of the following sample statistics must have remained the same after the correction was made? A. Mean B. Median C. Mode D. Range E. Variance

  31. #29 The equation of the least squares regression line for the points on the scatter plot above is . What is the residual for the point (3, 5)? A. 1.51 B. 3.00 C. 3.49 D. 5.00 E. 8.49

  32. #30 There were 100 rats put through a series of 3 mazes in a lab experiment. There were 36 rats that ran through maze A, 40 rats ran through maze B, and 28 rats ran through maze C. Twelve rats ran through both maze A and B, 15 rats ran through both maze B and C, 10 rats ran through both maze A and C, and 5 rats ran through all 3 mazes. What is the probability that a rat did not run through any of the mazes? • 16% • 23% • 28% • 40% • 72%

  33. Answers 1. B 11. D 21. C 2. B 12. C 22. C 3. A 13. A 23. C 4. D 14. A 24. B 5. D 15. E 25. D 6. C 16. E 26. D 7. B 17. D 27. B 8. D 18. C 28. B 9. C 19. E 29. A 10. B 20. A 30. C

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