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AP Statistics Fall Review (chapters 1-14) 1. The statistics below provide a summary of the distributions of heights, in inches, for a simple random sample of 200 young children. Mean: 46 inches Median: 45 inches Standard Deviation: 3 inches First Quartile: 43 inches Third Quartile: 48 inches About 100 children in the sample have heights that are (a) Less than 43 inches (c) Between 43 and 48 inches (e) More than 46 inches (b) Less than 48 inches (d) Between 40 and 52 inches 2. (a) (b) (c) In which of the following situations would it be most difficult to use a census? To determine what proportion of licensed bicycles on a university campus have lights To determine what proportion of students in a high school support wearing uniforms To determine what proportion of registered students enrolled in a college are employed more than 20 hours each week (d) To determine what proportion of single-family dwellings in a small town have tow-car garages (e) To determine what proportion of fish in Lake Michigan are bass 3. The distribution of the diameters of a particular variety of oranges is approximately normal with a standard deviation of 0.3 inch. How does the diameter of an orange at the 67th percentile compare with the mean diameter? (a) 0.201 inch below the mean (b) 0.132 inch below the mean (c) 0.132 inch above the mean (d) 0.201 inch above the mean (e) 0.440 inch above the mean 4. A fair coin is to be flipped 5 times. The first 4 flips land “heads” up. What is the probability of “heads” on the next (5th) flip of this coin? 1 1 4 1 5 1 4 1 (a) 1 (b) (c) ( ) ( ) ( ) (d) ( ) ( ) (e) 0 2 2 2 2 1 2 5. Let X represent a random variable whose distribution is normal, with a mean of 100 and a standard deviation of 10. Which of the following is equivalent to ( > 115)? (a) (b) (c) (d) (e) ( < 115) ( ≤ 115) ( < 85) (85 < < 115) 1 − ( < 85) 6. The stemplot below shows the yearly earnings per share of stock for two different companies over a sixteen-year period. Which of the following statements is true? (a) (b) (c) (d) (e) The median of the earnings of Company A is less than the median of the earnings of Company B. The range of the earnings of Company A is less than the range of the earnings of Company B. The third quartile of Company A is smaller than the third quartile of Company B. The mean of the earnings of Company A is greater than the mean of the earnings of Company B. The interquartile range of Company A is twice the interquartile range of Company B. 7. A television news editor would like to know how local registered voters would respond to the question, “Are you in favor of the school bond measure that will be voted on in an upcoming special election?” A television survey is conducted during a break in the evening news by listing two telephone numbers side by side on the screen, one for viewers to call if they approve of the bond measure, and the other to call if they disapprove. This survey method could produce biased results for a number of reasons. Which one of the following is the most obvious reason? (a) It uses a stratified sample rather than a simple random sample. (b) People who feel strongly about the issue are more likely to respond. (c) Viewers should be told about the issues before the survey is conducted. (d) Some registered voters who call might not vote in the election. (e) The wording of the question is biased. 8. A high school physics teacher was conducting an experiment with his class of the length of time it will take a marble to roll down a sloped chute. The class ran repeated trials in order to determine the relationship between the length, in centimeters, of the sloped chute and the time, in seconds, for the marble to roll down the chute. A linear relationship was observed and the correlation coefficient was 0.964. After discussing their results, the teacher instructed the students to convert all of the length measurements to meters but leave the time in seconds. What effect will this have on the correlation of the two variables? (a) Because the standard deviation of the lengths in meters will be one hundredth of the standard deviation of the lengths in centimeters, the correlation will decrease by one hundredth to 0.954. (b) Because the standard deviation of the lengths in meters will be one hundredth of the standard deviation of the lengths in centimeters, the correlation will decrease proportionally to 0.00964. (c) Because changing from centimeters to meters does not affect the value of the correlation, the correlation will remain 0.964. (d) Because only the length measurements have been changed, the correlation will decrease substantially. (e) Because meters are a much more common measurement for length in determining speed, the linear relationship of the data will be stronger and thus the correlation will increase substantially. 9. (a) (c) The table below shows the sample size, the mean, and the median for two samples of measurements. What is the median for the combined sample of 47 measurements? n Mean Median Sample I 21 42.6 45.0 Sample II 26 49.2 48.5 42.6+49.2 2 21(42.6)+26(49.2) 47 (b) (d) 45.0+48.5 2 21(45.0)+26(48.5) 47 (e) It cannot be determined from the information given. 10. A researcher wishes to test a new drug developed to treat hypertension (high blood pressure). A group of 40 hypertensive men and 60 hypertensive women is to be used. The experimenter randomly assigns 20 of the men and 30 of the women to the placebo and assigns the rest to the treatment. The major reason for separate assignment for men and women is that (a) It is a large study with 100 subjects (b) The new drug may affect men and women differently (c) The new drug may affect hypertensive and non-hypertensive people differently (d) This design uses matched pairs to detect the new-drug effect (e) There must be an equal number of subjects in both the placebo group and the treatment group 11. The histograms below represent the distribution of five different data sets, each containing 28 integers, from 1 through 7, inclusive. The horizontal and vertical scales are the same for all graphs. Which graph represents the data set with the largest standard deviation? 12. Lynn is planning to fly from New York to Los Angeles and will take the Airtight Airlines flight that leaves at 8 A.M. The Web site she used to make her reservation states that the probability that the flight will arrive in Los Angeles on time is 0.70. Of the following, which is the most reasonable explanation for how that probability could have been estimated? (a) By using an extended weather forecast for the date of her flight, which showed a 30% chance of bad weather. (b) By making assumptions about how airplanes work, and factoring all of those assumptions into an equation to arrive at the probability. (c) From the fact that, of all airline flights arriving in California, 70% arrive on time (d) From the fact that, of all airline flights in the United States, 70% arrive on time (e) From the fact that, on all previous days this particular flight had been scheduled, it had arrived on time 70% of those days. 13. One hundred people were interviewed and classified according to their attitude toward small cars and their personality type. The results are shown in the table below. Personality Type Type A Attitude Toward Small Cars Type B Total Positive 25 12 37 Neutral 11 9 20 Negative 24 19 43 Total 30 40 100 Which of the following is true? (a) Of the three attitude groups, the group with the negative attitude has the highest proportion of type A personality types. (b) Of the three attitude groups, the group with the neutral attitude has the highest proportion of type B personality types. (c) For each personality type, more than half of the 100 respondents has a neutral attitude toward small cars. (d) The proportion that has a positive attitude toward small cars is higher among people with a type B personality type than among people with a type A personality type. (e) More than half of the 100 respondents have a type A personality type and a positive attitude toward small cars. 14. A delivery service places packages into large containers before flying them across the country. These filled containers vary greatly in their weight. Suppose the delivery service’s airplanes always transport two such containers on each flight. The two containers are chosen so their combined weight is close to, but does not exceed, a specified weight limit. A random sample of flights with these containers is taken, and the weight of each of the two containers on each selected flight is recorded. The weights of the two containers on the same flight (a) (b) (c) (d) (e) Will have a correlation of 0 Will have a negative correlation Will have a positive correlation that is less than 1 Will have a correlation of 1 Cannot be determined from the information given 15. (a) (b) (c) (d) (e) Which of the following is NOT a characteristic of stratified random sampling? Random sampling is part of the sampling procedure. The population is divided into groups of units that are similar on some characteristic. The strata are based on facts known before the sample is selected. Each individual unit in the population belongs to one and only one of the strata. Every possible subset of the population, of the desired sample size, has an equal chance of being selected. 16. The weights of a population of adult male gray whales are approximately normally distributed with a mean weight of 18,000 kilograms and a standard deviation of 4,000 kilograms. The weights of a population of adult male humpback whales are approximately normally distributed with a mean weight of 30,000 kilograms and a standard deviation of 6,000 kilograms. A certain adult male gray whale weighs 24,000 kilograms. This whale would have the same standardized weight (z-score) as an adult male humpback whale whose weight, in kilograms, is equal to which of the following? (a) 21,000 (b)24,000 (c) 30,000 (d) 36,000 (e) 39,000 17. The histogram below displays the times, in minutes, needed for each chimpanzee in a sample of 26 to complete a simple navigational task. It was determined that the largest observation, 93, is an outlier since 3 + 1.5(3− 1 ) = 87.125. Which of the following boxplots could represent the information in the histogram? 18. A botanist is studying the petal lengths, measured in millimeters, of two species of lilies. The boxplots above illustrate the distribution of petal lengths from two samples of equal size, one from species A and the other from species B. Based on these boxplots, which of the following is a correct conclusion about the data collected in this study? (a) The interquartile ranges are the same for both samples. (b) The range for species B is greater than the range for species A. (c) There are more petal lengths that are greater than 70 mm for species A than there are for species B. (d) There are more petal lengths that are greater than 40 mm for species B than there are for species A. (e) There are more petal lengths that are less than 30 mm for species B than there are for species A. 19. Automobile brake pads are either metallic or nonmetallic. An experiment is to be conducted to determine whether the stopping distance is the same for both types of brake pads. In previous studies, it was determined that car size (small, medium, large) is associated with stopping distance, but car type (sedan, wagon, coupe) is not associated with stopping distance. This experiment would best be done (a) By blocking on car size (b) By blocking on car type (c) By blocking on stopping distance (d) By blocking on brake pad type (e) Without blocking 20. A group of students has 60 houseflies in a large container and needs to assign 20 to each of three groups labeled A, B, and C for an experiment. They can capture the flies one at a time when the flies enter a side chamber in the container that is baited with food. Which of the following methods will be most likely to result in three comparable groups of 20 houseflies each? (a) Label the first 20 flies caught as group A, the second 20 caught as group B, and the third 20 caught as group C. (b) Write the letters A, B, and C on separate slips of paper. Randomly pick one of the slips of paper and assign the first 20 flies caught to that group. Pick another slip and assign the next 20 flies caught to that group. Assign the remaining flies to the remaining group. (c) When each fly is caught, roll a die. If the die shows an even number, the fly is labeled A. If the die shows an odd number, the fly is labeled B. When 20 flies have been labeled A and 20 have been labeled B, the remaining flies are then labeled C. (d) Place each fly in its own numbered container (numbered from 1 to 60) in the order that it was caught. Write the numbers from 1 to 60 on slips of paper, put the slips in a jar, and mix them well. Pick 20 numbers out of the jar. Assign the flies in the containers with those numbers to group A. Pick 20 more numbers and assign the flies in the containers with those numbers to group B. Assign the remaining 20 flies to group C. (e) When each fly is caught, roll a die. If the die shows a 1 or 2, the fly is labeled A. If the die shows a 3 or 4, the fly is labeled B. If the die shows a 5 or 6, the fly is labeled C. Repeat this process for all 60 flies. 21. Two variables, x and y, were measured for a random sample of 25 subjects, and two separate regression models were fit to the data. Least squares estimation of the parameters in Model A yielded the following equation and residual plot. Least squares estimation of the parameters in Model B yielded the following equation and residual plot. Which of the following conclusions is correct? (a) (b) (c) (d) (e) Model A is appropriate, since the relationship between x and y is linear. Model B is appropriate, since the relationship between x and y is linear. Model A is appropriate, since the relationship between log x and log y is linear. Model A is appropriate, since the relationship between log x and y is linear. Model B is appropriate, since the relationship between x and log y is linear. 22. The dotplot below displays the total number of miles that the 28 residents of one street in a certain community traveled to work in one five-day workweek. Which of the following is closest to the percentile rank of a resident from this street who traveled 85 miles to work that week? (a) 60 (b) 70 (c) 75 (d) 80 (e) 85 23. A large simple random sample of people aged nineteen to thirty living in the state of Colorado was surveyed to determine which of two MP3 players just developed by a new company was preferred. To which of the following populations can the results of this survey be safely generalized? (a) Only people aged nineteen to thirty living in the state of Colorado who were in this survey (b) Only people aged nineteen to thirty living in the state of Colorado (c) All people lining in the state of Colorado (d) Only people aged nineteen to thirty lining in the United States (e) All people living in the United States 24. Janelle collected data on the amount of time in minutes each person in a large sample of customers spent in a local store. The data also included recording the gender of each customer. These data were used to generate the boxplots shown below. Which of the following statements is true? (a) The range in the amount of time in minutes males in the sample of customers spent in the store is approximately 40 minutes. (b) The mean amount of time in minutes males in the sample of customers spent in the store is approximately 20 minutes. (c) The third quartile of the amount of time in minutes males in the sample of customers spent in the store is approximately 45 minutes. (d) The interquartile range of the amount of time in minutes females in the sample of customers spent in the store is 15 minutes. (e) Approximately half of the males in the sample of customers spent at least as much time in the store as any female in the sample of customers. 25. The buyer for an electronics store wants to estimate the proportion of defective wireless game controllers in a shipment of 5,000 controllers from the store’s primary supplier. The shipment consists of 200 boxes each containing 25 controllers. The buyer numbers the boxes from 1 to 200 and randomly selects six numbers in that range. She then opend the six boxes with the corresponding numbers, examines all 25 controllers in each of these boxes, and determines the proportion of the 150 controllers that are defective. What type of sample is this? (a) Biased random sample (b) Nonrandom sample (c) Simple random sample (d) Stratified random sample (e) Cluster random sample 26. A distribution of test scores is not symmetric. Which of the following is the best estimate of the z-score of the third quartile? (a) 0.67 (b) 0.75 (c) 1.00 (d) 1.41 (f) This z-score cannot be estimated from the information given. 27. A certain type of remote-control car has a fully charged battery at the time of purchase. The distribution of running times of cars of this type, before they require recharging of the battery for the first time after its period of initial use, is approximately normal with a mean of 80 minutes and a standard deviation of 2.5 minutes. The shaded area in the figure below represents which of the following probabilities? (a) The probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 75 minutes and 82.5 minutes. (b) The probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 75 minutes and 85 minutes. (c) The probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 77.5 minutes and 82.5 minutes. (d) The probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 77.5 minutes and 85 minutes. (e) The probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 77.5 minutes and 87.5 minutes. 28. Which of the following scatterplots could represent a data set with a correlation coefficient of r = -1? 29. Publishers of a magazine wish to determine what proportion of the magazine’s 50,000 subscribers are pleased with their subscription. The publishers intend to mail a survey to 1,000 subscribers randomly selected from those who have received the magazine for 5 years or more. This introduces selection bias, since long-subscribing customers are more likely to be pleased with their subscription. Which of the following would best eliminate selection bias? (a) Mail surveys to 2,000 subscribers randomly selected from those who have received the magazine for 5 years or more. (b) Mail surveys to 1,000 subscribers randomly selected from those who have received the magazine for 1 year or less. (c) Mail surveys to 1,000 subscribers randomly selected from all subscribers. (d) Mail surveys to 1,000 subscribers randomly selected from those who have received the magazine for 5 years or more and 1,000 subscribers randomly selected from those who have received the magazine for 1 year or less. (e) Mail surveys to 500 subscribers randomly selected from a group who have received a free six-month subscription within the past year. 30. A data set of test scores is being transformed by applying the following rule to each of the raw scores. Transformed score = 3.5 (raw score) + 6.2 Which of the following is NOT true? (a) (b) (c) (d) (e) The mean transformed score equals 3.5(mean raw score) + 6.2. The median transformed score equals 3.5(the median raw score) + 6.2. The range of the transformed scores equals 3.5(the range of the raw scores) + 6.2. The standard deviation of the transformed scores equals 3.5(the standard deviation of the raw scores). The IQR of the transformed scores equals 3.5(the IQR of the raw scores). 31. A random sample of 25 households from the Mountainview School District was surveyed. In this survey, data were collected on the age of the youngest child living in each house hold. The histogram below displays the data collected in the survey. In which of the following intervals in the median of these data located? (a) 0 years old to less than 2 years old (c) 6 years old to less than 8 years old (e) 10 years old to less than 12 years old (b) 4 years old to less than 6 years old (d) 8 years old to less than 10 years old 32. In a recent survey, 60 randomly selected married couples from the same town were asked to rate the overall quality of living in their town on a scale from 1 (very poor) to 10 (excellent) on twenty different attributes such as accessibility to major highways, availability of entertainment, services provided by tax dollars, etc. For each couple, the husband’s individual ratings on the twenty attributes were averaged to produce an overall quality rating, and that process was repeated for the wife. Each point on the scatterplot below displays the overall rating of one of the 60 couples with the husband’s rating represented by the horizontal axis and the wife’s rating represented by the vertical axis. Based on the scatterplot, which of the following statements is true? (a) (b) (c) (d) (e) Husbands tend to rate the quality of living higher than their wives did. More overall ratings of 7 or less were assigned by husbands than by wives. The range in the husbands’ overall ratings is greater than the range in the wives’ overall ratings. The difference in overall ratings between a husband and wife was not more than 3 for any couple. For each couple, the overall rating assigned by the husband was the same as the overall rating assigned by the wife. 33. A new restaurant is interested in determining the best time-temperature combination for roasting a five-pound cut of lamb. The times to be tested are 45 minutes, 60 minutes, and 90 minutes at temperatures of 350 degrees Fahrenheit and 425 degrees Fahrenheit for each time, with the exception of the 90 minute-425 degree combination. That combination is being eliminated because it will overcook the lamb, which leaves five combinations remaining. From 10 identical cuts of lamb, 2 are randomly selected to roast using each of the timetemperature combinations in the same oven. The quality of the finished product is evaluated for each roast. Which of the following is true? (a) (b) (c) (d) (e) The explanatory variable is the quality of the finished lamb. The response variable is the roasting temperature for the lamb. If the experiment is repeated, identical results will be expected. There should be a control group (i.e. , a group in which no treatment is given). The two cuts that are being roasted for each time-temperature combination are an example of replication. Questions 34-35 refer to the following scenario and set of data. In the 1830s, land surveyors began to survey the land acquired in the Louisiana Purchase. Part of their task was to note the sizes of trees they encountered in their surveying. The table of data below is for bur oak trees measured during the survey. 34. Which of the following differenced in cumulative relative frequencies gives the proportion of trees that are 12 inches to 16 inches, inclusive, in diameter? (a) 0.615 – 0.325 (b) 0.615 – 0.473 (c) 0.726 – 0.325 (d) 0.726 – 0.473 (e) 0.731 – 0.325 35. An outlier may be defined as a data point that is more than 1.5 times the interquartile range below the lower quartile or is more than 1.5 times the interquartile range above the upper quartile. According to this definition, what is the diameter, in inches, of the smallest tree that is an outlier? (a) 4 (b) 28 (c) 30 (d) 34 (e) 36 36. The director of a fitness center wants to examine the effects of two exercise classes (spinning and aerobics) on body fat percentage. A six-week spinning class and a six-week aerobics class are offered at the same time and on the same days, so that a person can enroll in only one of them. A new class of each is about to begin, and each class has 25 people in it. Ten people are randomly selected from each class. Each person’s body fat percentage is measured at the beginning and again at the end of the six-week class. Using the change in body fat percentage as the response variable and conducting a test at the = 0.01 level, the director determines that there is a significant difference between the treatment means. Which of the following is a confounding variable in the study? (a) (b) (c) (d) (e) The director’s choice of spinning and aerobics classes as the types for use in the study The random sample of 10 people from each class The participants’ choice of which class to take The use of body fat percentage as the measure of effectiveness of the treatment The fact that both classes were conducted three times each week at the same time of day and for the same amount of time each day 37. The director of a technical school was curious about whether there is a relationship between students who complete one of the school’s most popular health sciences certificate programs and whether those students go on to complete more advanced studies in the health sciences within two years of completed the program. Data collected on these students are shown in the table below. Which of the following statements is true for these 100 students? (a) Being a person who completed more advanced studies is more likely than being a person who did not complete more advanced studies. (b) Being a person who completed the program is less likely than being a person who did not complete the program. (c) Being a person who completed the program and completed more advanced studies is less likely than being a person who did not complete the program and did not complete more advanced studies. (d) Being a person who did not complete the program but completed more advanced studies is less likely than being a person who completed the program and completed more advanced studies. (e) Being a person who completed the program but did not complete more advanced studies is more likely than being a person who did not complete the program and did not complete more advanced studies. 38. A dog food company wishes to test a new high-protein formula for puppy food to determine whether is promotes faster weight gain than the existing formula for that puppy food. Puppies participating in an experiment will be weighed at weaning (when they begin to eat puppy food) and will be weighed at one-month intervals for one year. In designing this experiment, the investigators wish to reduce the variability due to natural differences in puppy growth rates. Which of the following strategies is most appropriate for accomplishing this? (a) Block on dog breed and randomly assign puppies to existing and new formula groups within each breed. (b) Block on geographic location and randomly assign puppies to existing and new formula groups within each geographic area. (c) Stratify on dog breed and randomly sample puppies within each breed. Then assign puppies by breed to either the existing or the new formula. (d) Stratify on geographic location of the puppies and randomly sample puppies within each geographic area. Then assign puppies by geographic area to either the existing or the new formula. (e) Stratify on gender and randomly sample puppies within gender groups. Then assign puppies by gender to either the existing or the new formula. 39. In the scatterplot of y verses x shown below, the least squares regression line is superimposed on the plot. Which of the following points has the largest residual? (a) A (b) B (c) C (d) D (e) E 40. Exercise physiologists are investigating the relationship between lean body mass (in kilograms) and the resting metabolic rate (in calories per day) in sedentary males. (a) (b) (c) (d) (e) Based on the computer output above, which of the following is the best interpretation of the value of the slope of the regression line? For each additional kg of lean body mass, the resting metabolic rate increases on average by 22.56 calories/day. For each additional kg of lean body mass, the resting metabolic rate increases on average by 264 calories/day. For each additional kg of lean body mass, the resting metabolic rate increases on average by 144.9 calories/day. For each additional calorie/day for the resting metabolic rate, the lean body mass increases on average by 22.56 kg. For each additional calorie/day for the resting metabolic rate, the lean body mass increases on average by 264 kg.