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AP Statistics Exam Review: Multiple Choice 1st Semester 1. The standard deviation of 16 measurements of peoples weights (in pounds) is computed to be 5.4. The variance of these measurements is A) 2.24 B) 29.16 C) 52.34 D) 256 E) 21.6 Use the following to answer question 2: During the early part of the 1994 baseball season, many sports fans and baseball players noticed that the number of home runs being hit seemed to be unusually large. Below are separate stemplots for the number of home runs by American and National League teams. American League National League 2| 2|9 3|5 3|1 4|0 3 9 4|2 6 7 8 8 5|1 4 7 8 8 5|3 5 5 5 6|4 8 8 6|3 3 7 7|5 7 7| 2. Which of the following is a correct statement? A) The American League plot is reasonably symmetric. B) The National League plot is slightly skewed to the left. C) The median number of home runs hit by American League teams was higher than the median number hit by the National League teams. D) The mean number of home runs hit by American League teams was more than 6 higher than the mean for National League teams. E) All of the above. Use the following to answer question 3: A medical researcher collects health data on many women in each of several countries. One of the variables measured for each woman in the study is her weight in pounds. The following list gives the five-number summary for the weights of women in each of several countries. The first and last numbers for each country are the lower and upper deciles (10th and 90th percentiles). Country A: 100, 110, 120, 160, 200 Country B: 113, 135, 151, 185, 240 Country C: 84, 96, 110, 124, 136 Country D: 100, 143, 182, 191, 200 3. In one of the four countries, the mean weight of women is less than the median weight. Which country is it most likely to be? A) Country A B) Country B C) Country C D) Country D Use the following to answer question 4: For a physics course containing 10 students, the maximum point total for the quarter was 200. The point totals for the 10 students are given in the stemplot below. 11|6 8 12|1 4 8 13|3 7 14|2 6 15| 16| 17|9 4. The median point total for this class is A) 130 B) 130.5 C) 133 D) 134.4 E) 137 5. A reporter wishes to portray baseball players as overpaid. Which measure of center should he report as the average salary of major league players? A) The mean B) The median C) The mode D) Either the mean or median. It doesn’t matter since they will be equal. E) Neither the mean nor median. Both will be much lower than the actual average salary. 6. Using the standard normal distribution tables, the area under the standard normal curve corresponding to -0.5 < Z <1.2 is A) 0.3085 B) 0.8849 C) 0.5764 D) 0.2815 E) 0.3661 7. If the heights of 99.7% of American men are between 5.0’ and 7.0’, what is your estimate of the standard deviation of the height of American men? A) 1” B) 3” C) 4” D) 6” E) 12” 8. Birth weights at a local hospital have a normal distribution with a mean of 110oz. and a standard deviation of 15oz. The proportion of infants with birth weights under 95 oz. is A) 0.500 B) 0.159 C) 0.341 D) 0.841 E) 0.025 9. Using the standard normal distribution tables , the area under the standard normal curve corresponding to Z > -1.22 is A) 0.1151 B) 0.1112 C) 0.4129 D) 0.8849 E) 0.8888 10. 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) 5 B) 10 C) 15 D) 20 E) 25 11. The boxplots below summarize two data sets, X and Y. Which of the following MUST be true? We conclude that A) Set X and set Y have the same number of data points. B) The box of set X contains more data points than the box of set Y. C) The data in set X have a larger range than the data in set Y. D) About 50% of the values in set X are greater than about 75% of the values in set Y. E) The median of set X is less than the median of set Y. 12. Based upon a random sample of 30 seniors in a high school, a guidance counselor finds that 20 of these seniors plan to attend an institution of higher learning. A 90% confidence interval constructed from this information yields (0.5251, 0.80823). Which of the following is a correct interpretation for this interval? A) We can be 90% confident that 52.51% to 80.82% of our sample seniors plan to attend an institution of higher learning. B) We can be 90% confident that 52.51% to 80.82% of seniors at this high school plan to attend an institution of higher learning. C) We can be 90% confident that 52.51% to 80.82% of seniors in any school plan to attend an institution of higher learning. D) This interval will capture the true proportion of seniors from this high school who plan to attend and institution of higher learning 90% of the time. E) This interval will capture the proportion of seniors in our sample who plan to attend an institution of higher learning 90% of the time. 13. In this year’s city mathematics competition, a student scored 40; in last year’s competition, the student scored 35. The average score this year was 38 with a standard deviation of 2. Last year’s average score was 34 with a standard deviation of 1. In which year did the student score better? A) The student scored better on this year’s exam. B) The student scored better on last year’s exam. C) The student scsored equally well on both exams. D) Without knowing the number of test items, it is impossible to determine the better score. E) Without knowing the number of students taking the exam in the city, it is impossible to determine the better score. 14. Senior citizens make up about 12.4% of the American population. If a random sample of 200 Americans is selected, what is the probability that more than 180 of them are not senior citizens? 200 0.124 0.876 180 20 A) 180 200 0.876 0.124 180 20 B) 180 180 175.2 C) P z 0.124 200 0.9 0.124 D) P z (0.124)(0.876) 200 0.9 0.876 E) P z (0.124)(0.876) 200 15. Which of the following is not a condition for a geometric setting? A) There are only two possible outcomes for each trial. B) The probability of success is the same for each trial. C) The trials are independent. D) There are a fixed number of observations. E) The variable of interest is the number of trials required to reach the first success. 16. A young woman works two jobs and receives tips for both jobs. As a hair-dresser, her distribution of weekly tips has a mean $65 and a standard deviation $5.75. As a waitress, her distribution of weekly tips has a mean $154 and a standard deviation $8.02. What are the mean and standard deviation of her combined weekly tips? ( Assume independence for the two jobs.) A) mean $167.16; standard deviation $9.87 B) mean $167.16; standard deviation $13.77 C) mean $219.00; standard deviation $2.27 D) mean $219.00; standard deviation $9.87 E) mean $219.00; standard deviation $13.77 Use the following to answer questions 17 – 18: A business has two types of employees: managers and workers. Managers earn either $100,000 or $200,000 per year. Workers earn either $10,000 or $20,000 per year. The number of male and female managers at each salary level and the number of male and female workers at each salary level are given in the two tables below. Managers Workers Male Female Male Female $100,000 80 20 $10,000 30 20 $200,000 20 30 $20,000 20 80 17. The proportion of male managers who make $200,000 per year is A) 0.067 B) 0.133 C) 0.200 D) 0.400 E) 0.667 18. From these data we may conclude that A) the mean salary of female managers is greater than that of male managers. B) the mean salary of males in this business is greater than the mean salary of females. C) the mean salary of female workers is greater than that of male workers. D) this is an example of Simpson’s Paradox. E) All of the above. 19. A manufacturer constructs a 95% confidence interval for the average weight of the items he manufactures. His results need to be included in a report to his superiors, and the resulting interval is wider than he would like. In order to decrease the size of the interval the most , the manufacturer should take a new sample and A) increase the confidence level and increase the sample size. B) decrease the confidence level and increase the sample size. C) increase the confidence level and decrease the sample size. D) decrease the confidence level and decrease the sample size. E) The manufacturer will not be able to decrease the size of the interval. 20. A random sample of adults is taken in a rural county. Of the 120 adults sampled, 16 live in poverty. The poverty rate for the entire state is 8.9%. Is there statistical evidence to show that the poverty rate of this county is higher than that of the state? A) Since 13.33% is greater than 8.9%, there is sufficient evidence at the 0.05 level to show that the poverty rate of the county is higher than that of the state. B) Since 4.40% is less than 8.9%, there is insufficient evidence at the 0.05 level to show that the poverty rate of the county is higher than that of the state. C) Since 1.706 is less than 8.9, there is insufficient evidence at the 0.05 level to show that the poverty rate of the county is higher than that of the state. D) Since 1.706 is greater than 1.645, there is sufficient evidence at the 0.05 level to show that the poverty rate of the county is higher than that of the state. E) Since 0.044 is less than 0.05, there is insufficient evidence at the 0.05 level to show that the poverty rate of the county is higher than that of the state. 21. A candidate for mayor of Dallas calls 1,000 people chosen at random from the city telephone directory; 850 of them respond. What are the sampling frame and the sample in this example? A) Sampling frame: the telephone directory. Sample: the 850 people who respond. B) Sampling frame: the telephone directory. Sample: the 1,000 people who are called. C) Sampling frame: the 1,000 people who are called. Sample: the 850 people who respond. D) Sampling frame: all Dallas residents. Sample: the 1,000 people who are called. E) Sampling frame: all Dallas residents. Sample: the 850 people who respond. 22. The essential difference between an experiment and an observational study is that A) observational studies may have confounded variables, but experiments never do. B) in an experiment, people must give their informed consent before being allowed to participate. C) observational studies are always biased. D) observational studies cannot have response variables. E) an experiment imposes treatments on the subjects, but an observational study does not. 23. A simple random sample of 1200 adult Americans is selected, and each person is asked the following question: In light of the huge national deficit, should the government at this time spend additional money to establish a national system of health insurance? Only 39% of those responding answered yes. This survey A) is reasonably accurate because it used a large, simple random sample. B) probably overstates the percentage of people that favors a system of national health insurance. C) probably understates the percentage of people that favors a system of national health insurance. D) Is very inaccurate, but neither understates nor overstates the percentage of people that favors a system of national health insurance. Because simple random sampling was used, it is unbiased. E) Suffers from undercoverage bias. Use the following to answer question 24: 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 14873 24. The first three students in your sample have labels A) 955, 929, 400 B) 400, 769, 769 C) 559, 294, 007 D) 929, 400, 769 E) 400, 769, 335 25. In a box plot, if the left whisker is longer than the right whisker, the distribution of the data values will be A) positively skewed B) negatively skewed C) symmetric D) uniform E) back to Back time plots 26. I select two cards from a deck of 52 cards and observe the color of each. Which of the following is an appropriate sample space (S) for the possible outcomes? A) S = {red, black} B) S = {(red, red), (red, black), (black, red), (black, black)}, where, for example, (red, red) stands for the event “the first card is red and the second card is red.” C) S = {(red, red), (red, black), (black, black)}, where, for example, (red, red) stands for the event “the first card is red and the second card is red.” D) S = {0, 1, 2}. E) All of the above. Use the following to answer question 27: An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. 27. The conditional probability of A given B A) is 0.5 B) is 0.3 C) is 0.2 D) is 1/6 E) cannot be determined from the information given. 28. You read a book about bridge that the probability that each of the four players is dealt exactly one ace is about 0.11. This means that A) in every 00 bridge deals, each player has one ace exactly 11 times B) in one million bridge deals, the number of deals on which each player has one ace will scarcely be within 100 of 110,000. C) in a very large number of bridge deals, the percent of deals on which each player has one ace will be very close to 11%. D) in a very large number of bridge deals, the average number of aces in a hand will be very close to 0.11. 29. The collection of all possible outcomes of a random phenomenon is called A) a census B) the probability C) a chance experiment D) the sample space E) the distribution 30. If the knowledge that an event A has occurred implies that a second event B cannot occur, the events A and B are said to be A) independent B) disjoint C) mutually exhaustive D) the sample space E) complementary Use the following to answer question 31: The weight of medium-sized tomatoes selected at random from a bin at the local supermarket is a random variable with mean 10 and standard deviation 1 ounce. 31. Suppose we pick four tomatoes from the bin at random and put them in a bag. The weight of the bag is a random variable with a standard deviation (in ounces) of A) 0.25 B) 0.50 C) 1.0 D) 4.0 E) none of these, because the numbers are not independent 32. The probability distribution for the number of heads in four tosses of a coin is given by Number of Heads 0 1 2 3 4 Probability 0.0625 0.250 0.375 0.250 0.0625 Let X represent the number of heads. The probability of at least one tail is given by A) P( X 3) B) P( X 3) C) P( X 3) D) P( X 3) E) P( X 1) Use the following to answer question 33: A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution. X 0 1 2 3 4 P(X) 0.1 0.1 0.1 0.1 0.6 33. Suppose the store is open seven days per week from 8:00 a.m. to 5:30 p.m. The mean number of customers that make a purchase during the first hour that the store iss open during a one week period is A) 3.0 B) 9.0 C) 19.0 D) 21.0 E) 28.0 34. The weight of reports produced in a certain department has a normal distribution with mean 60g and standard deviation 12g. The probability that the next report will weigh less than 45g is A) .1056 B) .3944 C) .1042 D) .0418 E) .8944 Use the following to answer question 35: The probability density of a random variable X is given in the figure below 35. The probability that X is at least 1.5 is A) 0 B) 1/4 C) 1/3 D) 1/2 E) 3/4 Use the following to answer question 36: There are twenty multiple choice questions on an exam, each having responses a, b, c, or d. Each question is worth five points and only one option per question is correct. Suppose the student guesses the answer to each question, and the guesses from question to question are independent. 36. The distribution of X, the number of questions the student will get correct, is A) binomial with parameters n = 5 and p = 0.2. B) binomial with parameters n = 20 and p = 0.25 C) binomial with parameters n = 5 and p = 0.25 D) binomial with parameters n = 4 and p = 0.25 E) None of these 37. In a certain game of chance, your chances of winning are 0.2. If you play the game five times and outcomes are independent, the probability that you win all five times is A) 0.6723 B) 0.3277 C) 0.32 D) 0.04 E) 0.00032 38. As part of a promotion for a new type of cracker, free trial samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a packet of crackers after tasting the free sample is 0.20. Different shoppers can be regarded as independent trials. If X is the number of the next 100 shoppers that buy a packet of the crackers after tasting a free sample, then the probability that X is at most 25 is approximately A) 0.0438 B) 0.1056 C) 0.3773 D) 0.9125 E) 0.9562 Use the following to answer questions 39-40: A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let X denote the number in the sample that say they support the increase. Suppose that 40% of all adults in Ohio support the increase. 39. The probability that X is more than 650 is A) < 0.0001 B) < 0.001 C) < 0.01 D) 0.9960 E) none of these 40. The mean of X is A) 5% B) 360 C) 0.40 D) 600 E) 90