AP Statistics Chapter 5 (Mostly) Multiple Choice Questions
Convenience Sampling
Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below. Categorize each as simple random sample, stratified random sample, systematic sampling, cluster sampling, or convenience sampling. Instruct each MMH facility to survey 10 discharged patients this week and send in the results.
B.
Approximately 52 percent of all recent births were boys. In a simple random sample of 100 recent births, 49 were boys and 51 were girls. The most likely explanation for the difference between the observed results and the expected results in this case is A. bias B. variability due to sampling C. nonsampling error D. a sampling frame that is incomplete E. confounding
Cluster Sample
Identify the type of sampling used. A farmer divides his orchard into 50 subsections, randomly selects 4 and samples all the trees within the 4 subsections in order to approximate the yield of his orchard.
D.
To test the new effects of a new fertilizer, 100 plots were divided in half. Fertilizer A is randomly applied to one half, and B to the other. This is A. an observational study. B. a matched pairs experiment. C. a completely randomized experiment. D. a block design. E. none of the above. The answer is _________________ (Note: The 100 plots were divided by 50 plots using one fertilizer and 50 using the other not each of the 100 plots having a fertilizer on each half.)
E.
Which of the following statements is FALSE? A. Nonresponse can cause bias in surveys because nonrespondents often tend to behave differently from people who respond. B. Non-sampling errors are often bigger than the random sampling errors in surveys. C. Slight changes in the wording of questions can make a measurable difference in survey results. D. People will sometimes answer a question differently for different interviewers. E. Sophisticated statistical methods can always correct the results if the population you are sampling from is different from the population of interest, for example, due to undercoverage.
Cluster Sample
Identify the type of sampling used. In order to determine the average IQ of ninth-grade students, a school psychologist obtains a list of all schools in the local public school system. She randomly selects five of these schools and administers an IQ test to all ninth-grade students at the selected sample.
Systematic Sampling
Identify the type of sampling used. In order to estimate the percentage of defects in a recent manufacturing batch, a quality control manager at Intel selects every 8th chip that comes off the assembly line starting with the 3rd, until she obtains a sample of 140 chips.
Stratified Random Sample
Identify the type of sampling used. A member of Congress wishes to determine her constituency's opinion regarding estate taxes. She divides her constituency into three income classes: low-income households, middle-income households, and upper-income households. She then takes a random sample of households from each income class.
Voluntary Response Sample
Identify the type of sampling used. A radio station asks its listeners to call in their opinion regarding the use of American forces in peacekeeping missions.
Stratified Random Sample
Identify the type of sampling used. A school official divides the student population into five classes: freshman, sophomore, junior, senior, and graduate student. The official takes a random sample from each class and asks the members' opinions regarding student services.
Cluster Sample
Identify the type of sampling used. In an effort to determine customer satisfaction, United Airlines randomly selects 50 flights during a certain week and surveys all passengers on the flights.
E.
In the design of a survey, which of the following best explains how to minimize response bias? A. Increase sample size. B. Decrease sample size. C. Randomly select the sample. D. Increase the number of questions in the survey. E. Carefully word and field-test survey questions.
A.
The manager of a public swimming pool wants to compare the effectiveness of two laundry detergents, Detergent A and Detergent B, in cleaning the towels that are used daily. As each dirty towel is turned in, it is placed into the only washing machine on the premises. When the washing machine contains 20 towels, the manager flips a coin to determine whether Detergent A or Detergent B. will be used for that load. The cleanliness of the load of towels is rated on a scale of 1 to 10 by a person who does not know which detergent was used. The manager continues this experiment for many days. Which of the following best describes the manager's study? A. A completely randomized design. B. A randomized block design with Detergent A and Detergent B as blocks. C. A randomized block design with the washing machine as the block. D. A matched pairs design with Detergent A and Detergent B as the pair. E. An observational study.
B.
We wish to draw a sample of size 5 without replacement from a population of 50 households. Suppose the households are numbered 01, 02, ...,50, and suppose that the relevant line of the random number table is 11362 35692 96237 90842 46843 62719 64049 17823. Then the households selected are A. households 11 13 36 62 73 B households 11 36 23 08 42 C. households 11 36 23 23 08 D. households 11 36 23 56 92 E. households 11 35 96 90 46
A.
A recent survey b a large-circulation Canadian magazine on the contribution of universities to the economy was circulated to 394 people who the magazine decided "are the most likely to know how important universities are to the Canadian economy." The main problem with using these results to draw conclusions about the general public's perception is A. selection bias. B. insufficient attention to the placebo effect. C. no control group. D. nonresponse bias. E. interviewer bias.
A.
John thinks that whenever he takes the late bus home after school, he is hungrier than when he takes the regular bus home. He decides to record whether or not he goes back for seconds at the dinner table each night and cross reference those data with which bus he took home from school. He found that he had seconds at dinner eight of the nine recorded days in which he took the late bus compared to having seconds at dinner only seven of the 21 times he took the early bus. John turned in a paper to his statistics teacher that stated that the late bus was causing his hunger. When John's paper was returned to him, the professor had written, "Were the days you took the late bus the same days you played after-school sports?" What potential problem is his professor trying to point out? A. The possibility of a confounding variable. B. The low power of a test with a small sample size. C. The lack of blinding. D. The unequal sample size. E. The lack of a control group.
D.
A researcher conducting a telephone survey is concerned about possible sources of bias. Of the following, which is the best example of nonresponse bias? A. The wording of the questions in the survey leads people to respond in a certain way. B. The behavior of the interviewer leads people to respond in a certain way. C. People might be uncomfortable with the survey questions and, as a result, might not always respond to those questions truthfully. D. Many of the people selected to participate in the survey who do not respond might have different opinions from those who do respond. E. People without telephones are overlooked in the sampling procedure used to determine who is surveyed.
B.
At a large conference of teachers from a variety of subjects, a random sample of 50 mathematics teachers attending the conference was selected. Among the selected mathematics teachers, 28 percent had taken one or more courses in statistics. For which of the following populations is 28 percent a reasonable estimate of the percentage of those who have taken one or more course in statistics? A. All mathematics teachers. B. All mathematics teachers who attended the conference. C. All mathematics teachers who have taken one or more course in statistics. D. All teachers who attended the conference. E. All teachers.
Stratified Random Sample
Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below. Categorize each as simple random sample, stratified random sample, systematic sampling, cluster sampling, or convenience sampling. Randomly select some MMH facilities from each of the five geographic regions, and then take random samples from each of these hospital discharge lists.
D.
A CD manufacturer wanted to determine which of two different cover designs for a newly released CD will generate more sales. The manufacturer chose 70 stores to sell the CD. Thirty-five of these stores were randomly assigned to sell CDs with one of the cover designs and the other 35 were assigned to sell the CDs with the other cover design. The manufacturer recorded the number of CDs sold at each of the stores and found a significant difference between the mean number of CDs sold for the two cover designs. Which of the following gives the conclusion that should be made based on the results and provides the best explanation for the conclusion? A. It is NOT reasonable to conclude that the difference in sales was caused by the different cover designs because this was not an experiment. B. It is NOT reasonable to conclude that the difference in sales was caused the different cover designs because there was no control group for comparison. C. It is NOT reasonable to conclude that the difference in sales was caused the different cover designs because the 70 stores were not randomly chosen. D. It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores. E. It is reasonable to conclude that the difference in sales was caused by the different cover designs because the sample size was large.
A.
A Texas school district wants to compare the effectiveness of a standard AP Statistics curriculum and a new "hands-on" AP Statistics curriculum. Two experienced teachers, Mr. Pryor and Mr. Legacy each teach one class with the standard curriculum and one with the new approach. Students are assigned at random to these four classes. At the end of the year, all students take the AP Statistics exam. The Texas experiment has A. one factor: the AP Statistics curriculum a student is assigned to. B. has two factors: the AP Statistics curriculum and the teacher a student is assigned to. C. has two factors: the standard curriculum and one with the hands-on approach. D. has three factors: the math curriculum, the teacher, and the class a student is assigned to. E. has three factors: the standard curriculum, the hands-on approach, and the teacher a student is assigned to.
C.
A Texas school district wants to compare the effectiveness of a standard AP Statistics curriculum and a new "hands-on" AP Statistics curriculum. Two experienced teachers, Mr. Pryor and Mr. Legacy each teach one class with the standard curriculum and one with the new approach. Students are assigned at random to these four classes. At the end of the year, all students take the AP Statistics exam. The subjects in this experiment are A. Mr. Pryor and Mr. Legacy. B. the two AP Statistics curricula. C. the students in the four classes. D. all students taking AP Statistics in Texas. E. only one: AP Statistics.
B.
A certain library has 10,000 books. Two thousand of these books are nonfiction books and the rest are fiction. In order to estimate the total number of pages in their nonfiction books, two plans are proposed. Plan I: 1. Sample 50 books at random. 2. Estimate the mean number of pages per book using a confidence interval. 3. Multiply both ends of the interval by 10,000 to get an interval estimate of the total. Plan II: 1. Identify the 2,000 nonfiction books. 2. Sample 50 nonfiction books at random. 3. Estimate the mean number of pages for nonfiction books using a confidence interval. 4. Multiply both ends of the interval by 2,000 to get an interval estimate of the total. On the basis of the information given, which of the following is the better method for estimating the total number of pages in nonfiction books in the library? A. Choose plan I over plan II. B. Choose plan II over plan I. C. Choose either plan, since both are good and will produce equivalent results. D. Choose neither plan since neither estimates the total number of nonfiction pages. E. The plans cannot be evaluated from the information given.
E.
A class in marketing designs two videos advertising an expensive Mercedes sports car. They test the videos by asking fellow students to view both (in random order) and say which makes them more likely to buy the car. Mercedes should be reluctant to agree that the video favored in this study will sell more cars because A. there is no control group. B. there is no placebo. C. the study used a matched pairs design instead of a completely randomized design. D. this is an observational study, not an experiment. E. results from students may not generalize to the older and richer customers who might buy a Mercedes.
B.
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 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 living in the state of Colorado. D. Only people aged nineteen to thirty living in the United States. E. All people living in the United States.
D.
A newspaper wants to determine the level of support in a large town regarding the construction of a new library in a downtown location. Which one of the following would represent a stratified sampling method? A. Randomly selected four residential blocks in the town and ask everyone who lives on those blocks. B. Select every fourth person who enters the current library until the desired number of people is selected. C. Take an SRS of people from the city phone directory. D. Take a random sample of residents from each of the northwest, northeast, southwest, and southeast quadrants of the city. E. Number the residents of the town using the latest census data. Use a random number generator to pick the sample.
A.
A polling firm is interested in surveying a representative sample of registered voters in the United States. The firm has automated its sampling so that random phone numbers within the United States are called Each time a number is called, the procedure below is followed. - If there is no response or if an answering machine is reached, another number is automatically called. -If a person answers, a survey verifies that the person is at least 18 years of age. - If the person is not at least 18 years of age, no response is recorded, and another number is called. - If the person is at least 18 years of age, that person is surveyed. Some people claim the procedure being used does not permit the results to be extended to all registered voters. Which of the following is NOT a legitimate concern about the procedure being used? A. Registered voters with children under the age of 18 years may be underrepresented in the sample. B. Registered voters with unlisted telephone numbers may be underrepresented in the sample. C. Registered voters who have more than one telephone number may be overrepresented in the sample. D. Registered voters who live in households consisting of more than one voter may be underrepresented. E. People who are not registered to vote may bias the sample results.
B.
A properly conducted survey randomly selected 1,000 Canadians (from a total population of about 30 million) and 1,000 Americans (from a total population of about 300 million). Which of the following is FALSE? A. Random selection ensures that both samples are representative of their respective populations. B. If 2,000 Canadians and 2,000 Americans were selected for the study, we could be confident that the sample result would be more accurate. C. A smaller proportion of the American population has been chosen. Therefore, a particular person has a smaller chance of being selected in America than in Canada. D. A potential stratification variable for both countries could be location: eastern, middle, or western continental. E. Random digit dialing to select people for the survey could induce biases in the results if the characteristic of interest for the survey is related to income.
A.
A regional transportation authority is interested in estimating the mean number of minutes working adults in the region spend commuting to work on a typical day. A random sample of working adults will be selected from each of three strata: urban, suburban, and rural. Selected individuals will be asked the number of minutes they spend commuting to work on a typical day. Why is stratification used in this situation? A. To remove bias when estimating the proportion of working adults living in urban, suburban, and rural areas. B. To remove bias when estimating mean commuting time. C. To reduce bias when estimating mean commuting time. D. To decrease the variability in estimates of the proportion of working adults living in urban, suburban, and rural areas. E. To decrease the variability in estimates of the mean commuting time.
E.
A researcher wanted to estimate the average amount of money spent on extracurricular activities per school in a certain region. The researcher randomly selected 20 public schools and 20 private schools in the region to be used in the sample. Which of the following best describes the type of sample that was taken? A. A census B. A cluster sample C. A convenience sample D. A simple random sample E. A stratified random sample
E.
An art gallery wants to conduct a survey to see what type of offerings people are most interested in. It wants to begin with a simple random sample of 50 people who have previously purchased art at the gallery. Which of the following methods will produce a simple random sample? A. Survey the 50 most recent purchasers. B. Survey the 50 purchasers who have spent the most money at the gallery. C. Use random numbers to choose 10 people from each of the following 5 groups: those who have purchased (1) watercolors, (2) sculptures, (3) canvas, (4) photographs, (5) mixed media. D. Hold a brunch for previous customers and put comment cards at 50 randomly assigned seats. E. Number a list of all people who have previously made a purchase. Use a table of random numbers to choose 50 people from this list and survey them.
C.
An experiment will be conducted to determine whether children learn their multiplication facts better by practicing with flashcards or by practicing on a computer. Children who volunteer for the experiment will be randomly assigned to one of the two treatments. Because the children's gender may affect the outcome, there will be blocking by gender. After practice, the children will be given a test on their multiplication facts. Why will it be impossible to conduct a double-blind experiment? A. The experimenter will know whether the child is a boy or a girl and whether he or she used flash cards or the computer. B. The child will know whether he or she is a boy or a girl. C. The child will know whether he or she used flashcards or the computer. D. The person who grades the tests will know whether the child was a boy or a girl. E. The person who grades the tests will know whether the child used flashcards or the computer.
Simple Random Sample (SRS)
Identify the type of sampling used. In an effort to identify whether an advertising campaign has been effective, a marketing firm conducts a nationwide poll by randomly selecting individuals from a list of known users of the product.
D.
In a recent poll of 1,500 randomly selected eligible voters, only 525 (35 percent) said that they did not vote in the last election. However, a vote count showed that 80 percent of eligible voters actually did not vote in the last election. Which of the following types of bias is most likely to have occurred in the poll? A. Nonresponse bias B. Sampling Bias C. Selection Bias D. Response Bias E. Undercoverage Bias
Systematic Sampling
Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below. Categorize each as simple random sample, stratified random sample, systematic sampling, cluster sampling, or convenience sampling. At the beginning of the year, instruct each MMH facility to survey every 500th patient discharged.
Stratified Random Sample
Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below. Categorize each as simple random sample, stratified random sample, systematic sampling, cluster sampling, or convenience sampling. Obtain a list of patients discharged from all MMH facilities. Divide the patients according to length of hospital stay (3 days or less, 3-7 days, 8-14 days, more than 14 days). Draw simple random samples from each group.
Simple Random Sample
Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below. Categorize each as simple random sample, stratified random sample, systematic sampling, cluster sampling, or convenience sampling. Obtain lists of patients discharged from all MMH facilities. Number these patients, and then use a random number table to obtain the sample.
C.
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 survey 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.
C.
The Commonwealth of Virginia wants to determine how many more people would use the Chesapeake Bay Bridge-Tunnel if the price were lowered from $12 to $10 with a valid Virginia ID. At first it was suggested that the Department of Motor Vehicles ask a random sample of people in the state if they had used the bridge in the past and how likely they would be to use it in the future should the rate remain the same and should the rate decrease. But objections were raised that the majority of Virginians do not live close enough to the bridge to be likely to use the bridge regardless of the price. It was then suggested that the survey be conducted at the tollbooth to the bridge. Again, there were objections. This time, the complaint was that you would not reach those who had decided not to use the bridge. Finally, someone suggested that the 10 counties closest to the bridge be identified and the survey be conducted by selecting a random sample of drivers in these counties. Everyone agreed that this was the preferable method to use in order to gauge increased traffic that would be generated by a reduction in rate. For the final sampling method used, what is the population, and what is the sample? A. Sample: All drivers in Virginia, Population: All drivers who consider using the bridge B. Sample: All drivers who use the Chesapeake Bay Bridge, Population: All drivers in Virginia C. Sample: Selected drivers in the counties closest to the bridge, Population: All drivers in the counties closest to the bridge D. Sample: Selected drivers in the counties closest to the bridge, Population: All drivers in Virginia E. Sample: All drivers who do not currently use the bridge, Population: All drivers in Virginia
B.
The Commonwealth of Virginia wants to determine how many more people would use the Chesapeake Bay Bridge-Tunnel if the price were lowered from $12 to $10 with a valid Virginia ID. At first it was suggested that the Department of Motor Vehicles ask a random sample of people in the state if they had used the bridge in the past and how likely they would be to use it in the future should the rate remain the same and should the rate decrease. But objections were raised that the majority of Virginians do not live close enough to the bridge to be likely to use the bridge regardless of the price. It was then suggested that the survey be conducted at the tollbooth to the bridge. Again, there were objections. This time, the complaint was that you would not reach those who had decided not to use the bridge. Finally, someone suggested that the 10 counties closest to the bridge be identified and the survey be conducted by selecting a random sample of drivers in these counties. Everyone agreed that this was the preferable method to use in order to gauge increased traffic that would be generated by a reduction in rate. In switching from the first sampling method where people were randomly chosen from all drivers in Virginia to the final sampling method, the state researchers were attempting to address the problem of people who live far from the bridge not using it. In this circumstance, what is the best description of how proximity to the bridge impacts this study? A. It creates nonresponse bias. B. It is a variable that could influence the response. C. It defines the sampling frame. D. It creates outliers. E. It is used for clustering.
D.
When determining which students will represent their high school in a local competition, the principal selected two students at random from a list of all freshmen at the school, two students at random from all sophomores, two students at random from all juniors, and two students at random from all seniors. This is an example of A. Simple random sampling B. Cluster sampling C. Systematic Sampling D. Stratified Sampling E. Convenience Sampling