Quiz 1 Name Date 1. A magazine asks readers to write in saying whether they agree with a statement about dating. What, potentially, is the main problem with this survey? A. bias due to voluntary response B. too much variability in the opinions C. size bias D. a lurking variable E. bias due to judgment sampling 2. A medical doctor estimates the prevalence of broken arms by studying the records of his own patients. What, potentially, is the main problem with this study? A. bias due to voluntary response B. too much variability in the prevalence of broken arms C. measurement bias D. a lurking variable E. bias due to convenience sampling 3. Identify which type of sampling design is being used in each scenario. a. A school administrator randomly selects 12 classes from your school and then randomly selects 5 students from each class to study a school library issue. b. A school administrator uses random numbers to select a sample of 60 students from the roster of students enrolled in your school. c. A school administrator gets a sample of 60 students from your school by randomly selecting 15 freshmen, 15 sophomores, 15 juniors, and 15 seniors. d. A school administrator uses the roster of students enrolled in your school to select a sample of students by choosing a person randomly from among the first 20 and then taking every 20th name on the roster thereafter. 4. Which of these will produce a simple random sample from the given population? A. Students in a classroom of 36 students: Randomly select 6 students, one from each of 6 rows. B. U.S. Honda Civic owners: Select the first 1500 people who bought a Civic in the United States since January 1 of this year. C. Your statistics class: Select all students whose phone number begins with a randomly chosen digit. D. Teachers in your school: Select all teachers whose last name begins with a randomly chosen letter of the alphabet. E. Students who eat lunch in the school cafeteria: Make a list of students as they enter the cafeteria and randomly select 30 of them using a random number table. Statistics in Action Instructor s Resource Book Chapter 4 Quiz 1 43
Quiz 1 (continued) 5. Which of these is not a reason for using sampling rather than a census? A. Sampling can save time and money. B. Sampling always results in a representative sample. C. Sometimes everything in the sample must be destroyed. D. Sampling a smaller number of people can give better accuracy than trying to get a good answer from everyone in a large population. E. Sampling allows you to spend more time with each individual in the sample. 6. What are two advantages of using a stratified random sample over a simple random sample? 7. Explain how you would sample households in your neighborhood to estimate the average number of pets per household. 44 Chapter 4 Quiz 1 Statistics in Action Instructor s Resource Book
Quiz 2 Name Date 1. What is the key to reducing confounding in an experiment? 2. What is meant by the placebo effect? What can a researcher do to account for this effect? 3. Suppose pairs of identical twins agree to participate in an experiment to test the effect of salt on blood pressure. It is decided by a coin flip which of the twins will consume a high-salt diet and which will consume a low-salt diet. The response variable will be their blood pressure after ten weeks on the diet. This is an example of A. a completely randomized design B. a randomized paired comparison design (matched pairs) C. a randomized paired comparison design with repeated measures on the same subject D. stratification E. two-stage sampling 4. When the effects of two variables on a response variable cannot be distinguished from each other, the variables are said to be A. biased B. blocked C. confounded D. stratified E. outliers 5. To test a new skin rash drug, researchers decide to administer both the new drug and the standard drug, in random order, to each patient in the experimental study. That is, the researchers carrying out the study plan to use a randomized paired comparison design with repeated measures. What is the main weakness of this design? A. It did not use blocking. B. The resulting data would show evidence of too much within-treatment variability. C. The resulting data would show evidence of too much between-treatment variability. D. There was no control group. E. The effect of the first drug may not have worn off before the second drug was administered. 6. Explain how you could improve on the design outlined in Question 5. Statistics in Action Instructor s Resource Book Chapter 4 Quiz 2 45
Quiz 2 (continued) 7. Suppose you want to study the effect of calculator use (yes or no) on the mathematics course grade for sixth-grade students in your district s single middle school. In the upcoming school year, the middle school will have a total of 500 sixth-grade students. a. Suppose that you plan to ask each student whether he or she uses a calculator and then compare the mean mathematics course grade for each group. Is this an observational study or an experiment? Explain. b. Now suppose that you have been granted permission to randomly assign students to classrooms. At this middle school, there are 25 students per class. Describe an experiment for such a study using the classroom as the experimental unit. Be sure to describe all needed randomization, and identify the treatment(s) and the response variable. c. Name the primary source of within-treatment variation for your design. d. Briefly describe how you could change your experiment in part b to a randomized block design that would help account for the variation you described in part c. 46 Chapter 4 Quiz 2 Statistics in Action Instructor s Resource Book
Test A Name Date 1. What is the main purpose of random selection in a sample survey? 2. What is the main difference between an observational study and an experimental study? 3. Which of these is a source of bias that is not directly related to the sample selection method? A. using a sampling process for its convenience B. allowing volunteers to be in the sample C. the order in which the questions are asked D. using expert judgment in selecting the units for the sample E. the sampling frame 4. The main way to protect against confounding is to A. use an observational study B. assign treatments randomly to subjects C. use a placebo D. repeat the treatment on different units E. none of the above 5. Blocking will be effective if A. all units in one block receive the same treatment B. each subject receives all treatments C. units are grouped so that each block contains units that are different D. units are grouped so that each block contains units that are similar E. units are grouped so that each block is representative of the population 6. Suppose you are interested in knowing the average weekly allowance of children who attend the Maplewood elementary schools. You take a sample of students by first grouping their families by income levels (low, medium, and high) and then taking a random sample from each income group. This is an example of what kind of sampling design? A. systematic sample with random start B. single-stage cluster sample C. stratified random sample D. simple random sample E. two-stage cluster sample Statistics in Action Instructor s Resource Book Chapter 4 Test A 47
Test A (continued) 7. Which of these is the definition of a biased sampling method? A. a method that results in estimates that are too high (or too low) on the average B. a method that usually results in estimates that are too high (or too low) C. a method that allows people to decide for themselves whether to be in the sample D. a method that results in a simple random sample E. a method that results in nonrepresentative samples some of the time, but accurate estimates on the average 8. Compared to simple random sampling, stratified sampling can help accomplish several goals. Which of these goals does it not advance? A. reduce the variability associated with a statistic such as the sample mean B. reduce the sample size needed for a predetermined margin of error C. provide good information on each stratum D. make it unnecessary to use randomization E. make it easier to take a sample 9. Blocking in an experimental design is used primarily to A. eliminate the need for random assignment B. reduce confounding C. reduce the within-treatment variation D. eliminate the need for replication E. reduce the between-treatment variation 10. There are two types of bias in sampling problems: bias due to the improper selection of sampling units and bias due to incorrect response or nonresponse. Which of these is least likely to help protect against bias? A. random selection of sampling units B. cluster sampling as compared to simple random sampling C. following up with those who do not respond to the initial survey D. designing clear and unambiguous questions E. constructing a good sampling frame 11. Briefly describe an example in which size bias might be an important consideration when doing a study or taking a sample (other than the hospital example described in the student book). 12. These two variables are strongly associated. What possible lurking variables could be responsible for this association? I. the number of rescues at the local swimming hole II. the number of people at the local ice cream store 48 Chapter 4 Test A Statistics in Action Instructor s Resource Book
Test A (continued) 13. A mathematics education researcher was interested in determining the effects of class size (small, medium, or large) and the use of a traditional statistics textbook versus a new textbook. The researcher conducted her own experiment, assigning each combination of class size and type of textbook to two classes at each of five chosen schools. The average final grade for the class was then recorded at the end of the year. a. What are the factors? What are the levels? b. What are the treatments? c. What are the experimental units? How many are there? d. What is the response variable? 14. To test the taste of a new and improved potato chip, a researcher asks passersby on a sidewalk to taste the new chip and then two competitors chips (all unmarked and remarkably identical to the new chip) and choose the one they like best. Name two ways this study could be improved. Statistics in Action Instructor s Resource Book Chapter 4 Test A 49
Test B Name Date 1. What is the main purpose of random assignment in an experiment? 2. Give an example for which an observational study would be more appropriate than an experimental study. 3. Which of these is a source of bias that is directly related to the sample selection method? A. the way in which the questions are asked B. a subject s refusal to respond C. the order in which the questions are asked D. the use of expert judgment in selecting the units for the sample E. the inaccuracy of a measuring device 4. Which of these will help protect against bias? A. using a sampling process for its convenience B. allowing volunteers to be in the sample C. using randomization in choosing the units for the sample D. using expert judgment in choosing the units for the sample E. performing an observational study 5. Which of these is the main reason for using blocking in an experiment? A. to reduce between-treatment variation B. to reduce the within-treatment variation C. to reduce variability within each experimental unit D. to reduce confounding E. to eliminate the need for replication 6. Suppose you are interested in knowing the average weekly allowance of children who attend the Maplewood elementary schools. You take a sample of students by first taking a random sample of six classrooms and then taking a random sample from each selected classroom. This is an example of what kind of sampling design? A. systematic sample with random start B. single-stage cluster sample C. stratified random sample D. simple random sample E. two-stage cluster sample 50 Chapter 4 Test B Statistics in Action Instructor s Resource Book
Test B (continued) 7. Which of these is not an example in which size bias might be an important consideration? A. estimating the size of a college s biology classes by taking a simple random sample of students who are taking biology and then asking the student the size of his or her class B. estimating the average size of lakes in a state by drawing a line across a state map and measuring the size of all the lakes intercepted by the line C. estimating the average GNP for a country by randomly dropping a small number of grains of rice on a world map and then selecting those countries on which a grain falls D. estimating the average number of study hours for students at a local high school by first grouping their families by income levels and then taking a random sample from each income group E. finding the average length of string in a bag of strings by reaching in, mixing up the strings, selecting one, mixing them up again, selecting another, and so on 8. Which of these is the main characteristic of blocking? A. Subjects are grouped so that each block is representative of the population. B. Subjects are grouped so that each block contains subjects that are different. C. Subjects are grouped so that each block contains subjects that are similar. D. All subjects in one block get the same treatment. E. Blocking allows each subject to get all treatments. 9. Which of these is meant to help counteract the placebo effect? A. blinding the patient to which treatment he or she gets B. writing out a careful experimental protocol C. reducing between-treatment variability D. blocking E. replication 10. Which of these is not a purpose or a characteristic of an experiment? A. to compare two or more treatments B. to estimate the parameters of a fixed, well-defined population C. to establish cause and effect by comparing the effect of treatments on the response D. random assignment of treatments to subjects E. replication of each treatment on at least two subjects 11. In your own words, define a biased sampling method. Statistics in Action Instructor s Resource Book Chapter 4 Test B 51
Test B (continued) 12. In a northern state, these two variables are strongly associated. Each case is a week during the previous year. What possible lurking variable could be responsible for this association? I. the number of snow shovels sold at a local hardware store during the week II. the number of school closures during that same week 13. A botanist was interested in determining the effects of scheduled watering (three days a week or daily) and the use of fertilizer (no fertilizer, traditional, or organic) in hopes of increasing the heat rating of jalapeño peppers. The botanist conducted his own experiment, assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations that had similar soil and full sun. The average final heat rating for each plot was then recorded at the end of the growing season. a. What are the factors? What are the levels? b. What are the treatments? c. What are the experimental units? How many are there? d. What is the response variable? 14. To study the effects of fluorescent versus incandescent lighting on productivity in a small factory, a researcher compares weekly productivity measures for those employees currently working under fluorescent lighting with similar measures for those currently working under incandescent lighting. a. Is this an observational study or an experiment? b. Explain and provide details on how you would improve the design of this study. 52 Chapter 4 Test B Statistics in Action Instructor s Resource Book
AP Practice Quiz Name Date 1. The student council of your high school wants to conduct a survey regarding the dress code for school dances. You have advised them that it might be best to take a stratified random sample of the student body. Which of these is not a valid design using stratification? Two simple random samples are taken: one of the boys in the student body and the other of the girls in the student body. Four simple random samples are taken: one in each of the four grade levels. Three simple random samples are taken: one from students taking science, one from students taking math, and one from students taking neither of these subjects. Two random samples are taken: one of students whose GPAs are 2.5 or higher and the other of students whose GPAs are less than 2.5. All of these are valid designs using stratification. 2. A marketing company offers to pay $25 to the first 100 people who respond to its advertisement and complete a questionnaire regarding its client s product. This will produce which type of sample? simple random sample convenience sample voluntary response sample multistage cluster sample none of these 3. The three components of a well-designed experiment are comparison, randomization, and doubleblindness comparison, randomization, and replication comparison, replication, and simple random sampling randomization, replication, and homogeneity comparison, randomization, and homogeneity 4. In an experiment, if two variables are confounded, which of these statements is true? One of the variables must be a lurking variable. The variables will have a correlation coefficient greater than ±0.5. There is a clear indication that a placebo effect is present in the experiment. The investigator cannot separate the effect of the variables on a response variable. None of these is true. 5. Which of these is a reason for blocking? organize the treatment and control groups counteract the placebo effect produce groups that are homogeneous within the blocks allow for replication avoid the need for randomization 6. You work for a gym and have been asked to design an experiment to decide which of two types of exercise bikes is more attractive to customers. You have space for eight bikes in your exercise bike room, which will be placed as in the diagram. People enter the room by the door at the top of the diagram. There is a counter on each bike that records the number of hours it has been used. Television Door from Locker Rooms Television Space 1 Space 2 Space 3 Space 4 Space 5 Space 6 Space 7 Space 8 Design an experiment to compare the number of hours the two different brands of exercise bike are used that takes into account the fact that some bikes are in locations that make them more likely to be used than others when the gym isn t full. Statistics in Action Instructor s Resource Book Chapter 4 AP Practice Quiz 53
Chapters 2 4 AP Practice Quiz Name Date 1. Which of these statements is always true about a histogram? It is exactly the same as a bar graph. The exact value of the mean of the data can be calculated from the plot. The intervals defining the widths of the bars are segments of the real number line. The total area beneath all of the bars equals 1. All of the above are false. 2. Which data value, x, selected from the population with parameters given, has the higher z-score? I. x 25.4, 12.9, 3.7 II. x 137.5, 73.7, 17.1 I II The z-scores are equal. It cannot be determined, because you don t know the sample standard deviations. It cannot be determined, because you don t know if the populations are normally distributed. 3. Which of these statements would not be a correct interpretation of a correlation coefficient of r = 0.30? As the value of one variable gets bigger, the value of the other variable tends to get smaller. The coefficient of determination is 0.09. 30% of the variation in the response (y) is due to the explanatory variable (x). In a scatterplot of these data, all the points cannot lie on a straight line. All are correct. 4. Which of these plots could be a residual plot that indicates that the regression equation is a reasonable fit to the data? Residual 0 Residual Residual Residual 0 0 0 None of these indicates a reasonable fit. 5. A simple random sample was taken of large urban school districts throughout New England. The selected districts were identified as target districts. Within each district, a simple random sample of ten of its high schools was taken, and the principals of those high schools were interviewed. Which of these statements regarding the design is not true? This is an example of a two-stage cluster sample. Results from the interviews cannot be used to make inferences about the population of interest. The population of interest is the set of all high-school principals from large urban school districts in New England. Not every subset of principals has the same chance of being selected. All of these statements are true. 6. Which brand of chocolate chip cookies gives you the most chips per cookie? For the purpose of this question, take as your population all the cookies now in the nearest supermarket. Each cookie is a unit in this population. a. Explain why it would be hard to take a simple random sample. b. Describe how to take a cluster sample of chocolate chip cookies. c. Describe how you would get a two-stage cluster sample. What circumstances would make the two-stage cluster sample a better sample than the cluster sample? 54 Chapters 2 4 AP Practice Quiz Statistics in Action Instructor s Resource Book