AP STAT -- unit 3
A certain monthly magazine has both print and online subscribers. Print subscribers are people who pay to have the magazine physically delivered to them each month. Online subscribers are people who pay to have access to the electronic version of the magazine. The editors of the magazine want to study how online subscribers feel about the design of the electronic version, and they will gather data from a sample. Which of the following is a sample of the population of interest? A 50 subscribers to the magazine B 50 print subscribers C 50 online subscribers D 50 people who buy a copy of the magazine at a newsstand E 50 people who find an article in the magazine while searching online
Answer C Correct. The population of interest is subscribers to the electronic version of the magazine.
A market research firm is studying the effects of price and type of packaging on sales of a particular product. Twenty-seven stores with shoppers of similar characteristics will be used in the study. The nine combinations of three price levels and three packaging types are the treatments of interest. Total sales of the product over a seven-week period will be recorded. Which of the following describes the best design to use for the study? A A completely randomized design. Randomly assign the nine combinations of price level and packaging type so that three stores use each combination. B A completely randomized design. Randomly assign the three price levels so that nine stores use each price level. C A completely randomized design. Randomly assign the three packaging types so that nine stores use each type of packaging. D A randomized block design. Use packaging as a block. Randomly assign the nine combinations of three price levels and three packaging types so that three stores use each combination. E A randomized block design. Use packaging as a block. Randomly assign nine stores to each packaging type, then randomly assign price level to three stores within each block.
Answer A Correct. Because the stores have similar shoppers, a completely randomized design is appropriate. The description of the design, in which the combinations of treatments are randomly assigned to the stores, is correct.
A city has designed a survey to collect information about residents' opinions about city services. Which of the following describes a scenario in which nonresponse bias is likely present? A Surveys were mailed to 500 people, and 200 of the surveys were completed and returned. B Surveys were mailed to one-half of the neighborhoods in the city and all surveys were returned C Surveys were completed by the first 500 residents who listened to a radio show D Surveys were completed by 500 residents selected at random E Surveys were given to all residents in one neighborhood of the city and all surveys were returned
Answer A Correct. Since only 200 surveys out of the 500 surveys mailed were completed and returned, this high nonresponse rate is likely to lead to nonresponse bias.
Carla wants to investigate whether a person's political party affiliation causes the person to be more vocal about political issues. She plans to administer a survey to a large sample of people. Which of the following describes why the method of data collection used will prevent Carla from achieving her goal? A Surveys are not a valid method of collecting data. B Causation cannot be determined from a survey. C Political opinions are less likely to be voiced on a survey. D Carla needs to administer the survey to the entire population to determine causation. E Some surveys might not be returned, which could result in bias.
Answer B Correct. Causation is determined only through experiments, not observational studies, which includes surveys
A city planner is investigating traffic congestion at a certain intersection. To collect data, a camera will record the number of cars that pass through the intersection at different hours of the day and on different days of the week. Which of the following best describes the type of investigation being conducted by the city planner? A The investigation is an experiment because the cars go through the intersection at random. B The investigation is an experiment because the hours and the days are the treatments and the cars are the units. C The investigation is an observational study because treatments are not imposed. D The investigation is an observational study because only a sample of cars can go through the intersection on any given day. E The investigation is a sample survey because the cars that are recorded will inform the city planner about the population of cars on city roads.
Answer C Correct. No treatments are imposed or assigned to the cars. The number of cars going through the intersection is observed
A school nutritionist was interested in how students at a certain school would feel after taking a nutritional supplement. The nutritionist selected a random sample of twenty students from the school to participate in the study. Participants were asked to keep a journal on how well they felt after taking the supplement each day. What possible source of bias is present in the method of data collection? A Bias from a sampling method that only uses volunteers B Undercoverage bias C Nonresponse bias D Response bias where responses are self-reported E Response bias where the question wording is leading or confusing
Answer D Correct. The participants were asked to assess and record how they felt, making it more likely they could overestimate or underestimate the effects of the supplement.
A researcher selects a simple random sample of 1,200 women who are students at Midwestern colleges in the United States to use for an observational study. Which of the following describes the population to which it would be most reasonable to generalize the results? A All students in the United States B All college students in the United States C All women who are students in the United States D All students at Midwestern colleges in the United States E All women who are students at Midwestern colleges in the United States
Answer E Correct. Since this sample was taken from all women who are students at Midwestern colleges in the United States, generalizations can be made about all women who are students at Midwestern colleges in the United States.
Which of the following does not describe a sampling method that has a potential source of voluntary response bias for the administration of a survey about college athletics at a university? A Giving the survey to 30 students selected at random from each of the eight dorms on campus B Giving the survey to the first 50 students who call the university radio station after the broadcaster announces the survey on air C Giving the survey to any student who stops at a table set up in the student union after the survey is advertised D Giving the survey to all students who respond to an advertisement in the student newspaper E Giving the survey to physical education majors who receive extra credit for completing the survey
Answer A Correct. Since the 30 students are selected at random, they are not volunteers, so the selection of those students is not a likely source of voluntary response bias.
The quality-control manager of a large factory is concerned about the number of defective items produced by workers. Thirty workers at the factory agree to participate in a study of three different incentive plans to help reduce the number of defective items produced. The plans will be randomly assigned to the workers so that 10 workers received each plan. The reduction in the number of defective items produced by each worker will be recorded two weeks after the plans are implemented. Which of the following best describes why a completely randomized design is an appropriate design to use in this situation? A There is no blocking variable, and incentive plans will be randomly assigned to the workers. B There is no blocking variable, and the workers were selected at random. C Each incentive plan is a block, and a completely randomized design is not blocked. D Each plan will be randomly assigned to 10 pairs of workers who share a similar characteristic. E The number of workers participating in the study was greater than or equal to 30.
Answer A Correct. The treatments, which are the incentive plans, will be randomly assigned to the 30 workers
A researcher wanted to study the effects of a certain chemical on cell growth. The chemical was to be applied at two different doses, high and low, to two different cell types, strain A and strain B. Each combination of dose and cell type was to be replicated ten times. To have consistency from one replicate to the next, the researcher decided to use four lab technicians. One technician would be assigned the high dose with strain A. A second would be assigned the low dose with strain A. A third would be assigned the high dose with strain B. A fourth would be assigned the low dose with strain B. The assignment of lab technician to the replicates for a combination of dose and cell type would be randomized. A statistician told the researcher that the design could be improved by controlling confounding variables. Which of the following is potentially a confounding variable in this study? A Chemical used B Lab technician C Dose D Cell type E Cell growth
Answer B Correct. The different lab technicians may apply the chemical differently, thus affecting the response. One cannot determine whether the combination of the dose and cell type or the lab technician is affecting the response.
A researcher conducted an experiment to study the effects of an herbal supplement on the duration of the common cold. From a sample of 50 people who had a cold, the researcher assigned 25 people to take the supplement each day. The other 25 people were asked to drink water each day and were not given the supplement. The researcher recorded the number of days the cold lasted for each person. What are the experimental units of the study? A All people with a cold B The sample of 50 people who had a cold C The 25 people who were given the herbal supplement D The 25 people who were asked to drink water and were not given the supplement E The recorded number of days that the cold lasted for each person
Answer B Correct. The experimental units are all the people who participated in the study.
A certain county school district has 15 high schools. The high school seniors' plans after graduation in each school vary greatly from one school to the next. The county superintendent will select a sample of high school seniors from the district to survey about their plans after graduation. The superintendent will use a cluster sample with the high schools as clusters. A random sample of 5 high schools will be selected, and all seniors at those high schools will complete the survey. What is one disadvantage to selecting a cluster sample to investigate the superintendent's goal? A Cluster sampling is usually very expensive to implement and could cost the district too much money. B Because every senior in the selected clusters will complete the survey, the sample will be too large to yield accurate results. C The schools in the cluster sample might not be representative of the population of seniors. D There could be seniors absent from school on the day the survey is given, which could affect the results. E There is no disadvantage to using a cluster sample.
Answer C Correct. Because of the known difference between schools in terms of plans after graduation, the schools not chosen may have seniors that differ in some way from the seniors in schools that are chosen. Therefore, the plans of the students surveyed may not accurately represent the population in the district.
To estimate the percent of red marbles in a large bag of marbles, Margo will use the following sampling method. She will randomly select a marble, record its color, put it back into the bag, shake the bag to thoroughly mix the marbles, and then repeat those steps. She will perform the procedure many times. What type of sampling method is Margo using? A Cluster sampling B Stratified random sampling C Systematic random sampling D Random sampling with replacement E Random sampling without replacement
Answer D Correct. Each marble selected is randomly selected, so the sampling is random. Since the chosen marble is placed back into the bag before the next selection of a marble, the sampling is done with replacement. Margo is using random sampling with replacement.
At a certain clothing store, the clothes are displayed on racks. The clothes on each rack have similar prices, but the prices among the racks are very different. To estimate the typical price of a single piece of clothing, a consumer will randomly select four pieces of clothing from each rack. What type of sample is the consumer selecting? A A census B A cluster sample C A simple random sample D A stratified random sample E A systematic random sample
Answer D Correct. The pieces of clothing in the store are divided into strata, where each stratum is a rack of clothes having similar prices. The mean price calculated using the randomly selected pieces of clothing from the strata is an example of using a stratified random sample
An observational study found that the amount of sleep an employee gets each night is associated with job performance. The correlation coefficient was found to be r=0.86. A reader of the study concluded that more sleep causes employees to perform better. Why is such a conclusion not correct? A The correlation value should equal 1 for such a conclusion. B The correlation value should be negative for such a conclusion. C The sample was not representative of the population. D Causation cannot be determined from an observational study. E The correlation value implies that less than 75% of the variability in job performance can be explained by sleep.
Answer D Correct. The study was observational; causation can only be determined from an experiment.
A local employer asked for help selecting a new type of desk chair. Thirty employees volunteered, and each employee used the new desk chair for two weeks and the current desk chair for two weeks. To determine which chair was used first, a coin was flipped for each employee. Heads represented using the new chair first, and tails represented using the current chair first. At the end of each two-week period, the employees were asked to rate their satisfaction with the new chair. Which of the following best describes this study? A It is not a well-designed experiment because employees were allowed to volunteer instead of being randomly selected. B It is not a well-designed experiment because only one new chair was used. At least two new treatments must be used. C It is not a well-designed experiment because each employee was assigned both treatments, and each employee should be assigned only one. D It is not a well-designed experiment because using a coin flip does not guarantee that fifteen employees will use each chair first. E It is a well-designed experiment because there is random assignment, replication, and comparison of at least two treatment groups.
Answer E Correct. Random assignment, replication, and the ability to compare at least two treatment groups are all criteria for a well-designed experiment.
A researcher is studying the effect of genetically modified (GM) and nongenetically modified (nGM) corn on the weight gain of lambs. The sex and genetics of the lambs can affect their weight gain. Five sets of male twin lambs and five sets of female twin lambs—for a total of twenty lambs—are available for the study. The lambs will be randomly assigned to a diet of either GM or nGM diet of corn. Weight gain will be recorded for each lamb after five weeks on the diet. Which of the following designs would be best to use in the study? A A completely randomized design. Randomly assign ten lambs to the GMGM diet and ten lambs to the nGMnGM diet. B A stratified randomized design. Divide the lambs into males and females. Within each group, randomly assign the GMGM diet to one half and the nGMnGM diet to the other half. C A randomized block design. Randomly assign ten lambs to the GMGM diet and ten lambs to the nGMnGM diet. D A randomized block design. Randomly assign the GMGM diet to the male lambs and the nGMnGM diet to the female lambs. E A matched pairs design. For each set of twins, randomly assign one twin to the GMGM diet and the other twin to the nGMnGM diet.
Answer E Correct. Twin lambs are matched because they are the same sex and have similar genetic factors that affect weight gain. Randomly assigning one twin to each diet provides the best way of investigating the effects of the diet.
Eighteen individuals who use a particular form of social media were assigned a new user interface to use when logging in to their accounts. After using the new user interface for a week, each individual was asked to rate how easy or hard the new user interface was to use on a scale from 1 (extremely easy) to 9 (extremely hard). Which of the following correctly identifies why this is not a well-designed experiment? A There was a lack of control because not all individuals in the study used login passwords of the same length. B The individuals may not have been randomly selected. C There was not enough replication because the individuals used the new user interface for only one week. D There was a lack of control because not all individuals in the study use social media. E The study was not comparative—only one treatment was used.
Answer E Correct. Well-designed experiments should involve comparisons of at least two treatment groups, one of which could be a control group.