Test Bank For Introduction to Statistics and Data Analysis 5th Edition By Peck

Chapter 1: The Role of Statistics Name ___________________________ 1. Briefly describe how populations and samples differ. 2. In a psychological study of distance perception, introductory psychology class volunteers were given 5, 10, or 15 extra credit points depending on their level of participation in the experiment. They walked along paths laid out along hallways in the psychology building, and were asked to judge the distance they had walked. Each path distance was between 100 and 200 feet in length, and contained from two to seven 90 degree turns. The investigators also kept track of class standing (freshman, sophomore, junior, or senior). For each of the variables in this study, determine whether it is categorical or numerical. For each numerical variable, determine whether it is discrete or continuous: a) The true length of the path b) The amount of credit given to the volunteers c) The length of the path as judged by the students d) The number of 90 degree turns e) Class standing Chapter 1 Test, Form B Page 1 of 4 3. The most important right and responsibility of citizens in a democratic society is voting. The bar chart below shows, for different age groups in the 2000 presidential election in the United States, the percentage of individuals in that age group who are registered to vote. Voting in the 2000 Elections 0 -+ Age group % Registered (a) Describe in a few sentences the registration pattern that you see in the data above. (b) Some individuals argue that the reason for the current level of registration in the 18- 24 year-old group is that many of them are college students and would have to vote absentee. In your opinion, would that explain the registration level for the 18 – 24 age-group? Why or why not? Chapter 1 Test, Form B Page 2 of 4 % Registered 4. Artificial nest have often been used when biologists study predation on birds. It is usually assumed that predators will respond to artificial nests in the same way they do to real birds’ nests. A recent experiment was performed to check this assumption for predators of the American robin (Turdus migratorius) by comparing the egg loss in three experimental treatments: (1) natural robin’s nests, (2) artificial wicker-basket nests placed 30 meters in a random direction from natural robin’s nests, and (3) artificial wicker-basket nests placed in a 180 m by 240 m grid around robin’s nests. The data below are cumulative counts of eggs predated (stolen or broken and eaten) at 5, 10, and 15 day points of the experiment. Cumulative count of depredated eggs Nest type Natural robin 30 m from robin Grid 48 7 32 44 (a) Construct a bar chart to display the cumulative counts for the natural robin nests at their 5-, 10-, and 15-day checks. Original n 27 27 Day 5 check 12 3 Day 10 check 17 12 Day 15 check 19 18 (b) Fill in the relative frequency distribution (table) representing the cumulative counts for the artificial nests in the grid. (Do not convert the table to a graph.) Nest type Natural robin 30 m from robin Grid Original n 27 27 48 Day 5 check Day 10 check Day 15 check Chapter 1 Test, Form B Page 3 of 4 5. Biologists know that bats have different flight characteristics. Some bats exhibit fast, straight, and long flights; others are moderately slow, and highly maneuverable. The flight capabilities of bats are presumably a function of (a) the characteristics of the bat wings, and (b) the laws of physics. The data presented below are wing weights in grams for certain species of bats from Nicaragua and Costa Rica. Two categories of bat species are represented: fruit-eaters and insect-eaters. Fruit eaters: 9.9, 11.5, 47.0, 59.6, 18.2, 22.1, 22.9, 15.0, 15.4, 13.3, 38.3, 42.2, 114.3, 105.4, 80.9 Insect eaters: 23.8, 16.1, 4.2, 3.9, 7.5, 3.5, 3.9 a) Construct two dot plots that will allow you to easily compare the distributions of the wing weights for the two categories of bats, fruit-eaters and insect-eaters. b) Write a short paragraph describing the features of the two plots; what do these plots tell you about the differences in wing weight for fruit- and insect-eaters? Chapter 1 Test, Form B Page 4 of 4 Chapter 1 Test, Form B Answer Key 1. A population consists of an entire group about which some information is desired. A sample consists of only some part of this group that has been selected for study. 2. a) Numerical, continuous b) Numerical, discrete c) Numerical, continuous d) Numerical, discrete e) Categorical 3. (a) The proportion of people registering is smallest for the 18-24 year-old group, and gets larger with age, until finally declining in the 75+ year-old group. (b) Voting by absentee ballot may be more of a hassle b/c you have to get the ballot, but actual registration could be done at home before going to college. It would seem that unless the 18-24 year-olds decide for some reason they will not vote in their college years because of expected hassle of voting, the future voting would not be affecting the registration level. 4. (a) 20 15 10 5 0 Eggs Predated -- Natural nests 10-day check 5-day check 15-day check (b) Nest type Original n Natural robin 27 30 m from robin 27 Grid 48 Day 5 check 0.146 Day 10 check 0.667 Day 15 check 0.917 Chapter 1 Test, Form B Answer Key Page 1 of 2 Egg count 5. a) Fruit Eaters wing weight: Insect Eaters wing weight: 125 Wing Weight 125 Wing Weight b) The fruit eating bats have wings that are generally heavier than those of the insect eating bats. They are also much more spread out in weight, ranging from 9.9 to 114.3 grams. The insect-eating bats only have a range of 3.5 to 23.8 grams. Chapter 1 Test, Form B Answer Key Page 2 of 2 Chapter 2: Collecting Data Concept Quiz Name _________________________ The following questions are in a True / False format. The answers to these questions will frequently depend on remembering facts, understanding of the concepts, and knowing the statistical vocabulary. Before answering these questions, be sure to read them carefully! 1. 2. 3. 4. TF 5. 6. TF 7. 8. 9. 10. TF TF TF TF By definition, a simple random sample of size n is any sample that is selected in a manner to guarantee every individual in the population has an equal chance of selection. Clusters are non-overlapping subgroups of a population that have been identified as homogeneous. Blocking is a technique that can be used to filter out the effects of extraneous factors. Response bias can occur when responses are not actually obtained from all individuals selected for inclusion in the sample. Selection bias can occur if volunteers only are used in a study. Increasing sample size will generally eliminate bias in a sample. TF Stratified sampling is a sampling method that in no way involves simple random sampling. TF TF TF A placebo is identical in appearance to the treatment of interest, but contains no active ingredients. A study is an observational study if the investigator observes the behavior of a response variable when one or more factors are manipulated. In a well-designed experiment, the factors are confounded whenever possible. Chapter 2, Concept Quiz Page 1 of 2 Chapter 2: Collecting Data Concept Quiz (Cont'd) TF TF TF TF TF As long as the sample size is small relative to the population, there is little practical difference between sampling with replacement and sampling without replacement. A treatment is any particular combination of values for the explanatory variables. Two factors are extraneous if their effects on the response variable cannot be distinguished from one another. Random assignment to treatments will guarantee groups that are exactly alike for experimental purposes. The method of control wherein an extraneous variable is held constant is called blocking. 11. 12. 13. 14. 15. TF 16. TF 17. 18. 19. 20. Random subpopulations of a population are called strata. A control group provides a baseline for comparison to a treatment group. TF TF TF Random assignment of volunteers should result in comparable experimental groups. If the subjects as well as the person measuring the response are aware of the treatment assigned to the subject, only single-blinding is being used. Replicating in an experiment means that the number of subjects is greater than 1. Chapter 2, Concept Quiz Page 2 of 2 Chapter 2, Concept Quiz 1. F 2. F 3. T 4. F 5. T 6. F 7. F 8. T 9. F 10. F 11. T 12. T 13. F 14. F 15. F 16. F 17. T 18. T 19. F 20. T Answer Key Chapter 2, Concept Quiz Answer Key Page 1 of 1 Chapter 2: Collecting Data Section 2.1-2.2 Name ___________________________ 1. A friend of yours, who is not taking statistics, wonders why it is that anyone would choose to take a sample. "Obviously," she says, "you would get better information from a census." In a short paragraph, explain why it is that statisticians take samples rather than taking a census. 2. The most basic sampling method studied in statistics is the simple random sample (SRS). In your own words, what is the correct definition of a simple random sample of size n? Chapter 2, Quiz 1, Form A Page 1 of 4 3. The ZZZ chain of motels has a standard method of constructing their rooms to maximize the ease of parking for its customers. The rooms are arranged in adjacent buildings so that each customer can park outside the rented room. The layout for one of the with 48 rooms located along a famous highway is diagrammed below: Building A Building B Route 66 N E The manager would like to survey customers in 12 of his rooms (one randomly selected customer for each room selected in the sample) to assess their satisfaction with the motel services. The surveys will be placed on the customers' beds before they check in to the motel. In order to make the directions easy to follow, he elects to use systematic sampling. a) Explain how you would use random numbers to set up the systematic sampling process. Chapter 2, Quiz 1, Form A Page 2 of 4 b) Write a short paragraph for the maids that helps them carry out your method in part (a). Chapter 2, Quiz 1, Form A Page 3 of 4 4. Bias is a serious problem that sometimes arises when one takes a sample. a) In a few sentences, explain generally what bias is. b) What is the distinction between response bias and non-response bias? Chapter 2, Quiz 1, Form A Page 4 of 4 Chapter 2, Quiz 1, Form A Answer Key 1. Although we may get better information from a census, it is usually far too costly and time consuming to contact every member of the population. A large random sample will be nearly as good for far less cost. 2. A simple random sample of size n is a sample that is selected from a population in a way that ensures that every different possible sample of the desired size has the same chance of being selected. Note: It is important that students not only state that each person has the same chance of being chosen, but also each possible sample of size n has the same chance of being chosen. 3. a) Since there are 48 units in the population and we want a sample of size 12, we want to choose every fourth room after randomly choosing one of the first four rooms to start with. If we are using a random digit table, we would go through the table until we get a number from 1 to 4. Then, we would keep adding 4 to that number until we get to the end of the hotel rooms. For example, if we come upon the number 3 first, we would survey the 3rd room, the 7th room, the 11th room, etc. b) Dear Maids, when you are placing the surveys in the rooms, please follow the following procedure. Starting at the northwest corner of building A and moving east, place a survey in the third room, the seventh room, and every fourth room thereafter, moving back and forth along the four rows of rooms. 4. a) Bias is the tendency for a sample to differ from the corresponding population in some systematic way. b) Non-response bias occurs when responses are not actually obtained from all individuals selected for the sample. With response bias, however, responses are obtained from the subjects, but the method of observation tends to produce values that systematically differ from the true population value in some way. Chapter 2, Quiz 1, Form A Answer Key Page 1 of 1 Chapter 2: Collecting Data Section 2.1-2.2 Name ___________________________ 1. A friend of yours, who is not taking statistics, wonders why it is that anyone would choose to take a sample. "Obviously," he says, "you would get better information from a census." In a short paragraph, explain why it is that statisticians take a sample rather than a census. 2. The most basic sampling method studied in statistics is the simple random sample (SRS). In your own words, what is the correct definition of a simple random sample of size n? Chapter 2, Quiz 1, Form B Page 1 of 4 3. The ZZZ chain of motels has a standard method of constructing their rooms to maximize the ease of parking for its customers. The rooms are arranged in two adjacent buildings so that each customer can park outside the rented room. The layout for one of the motels in the chain along a famous highway is diagrammed below: Route 66 N E Building A Building B The manager would like to survey customers in 12 of his rooms (one randomly selected customer for each selected room) to assess their satisfaction with the motel services. As he tries to decide what sampling strategy is appropriate, the manager realizes that the rooms in Building A might be noisier than Building B, and this should be taken into account. a) What sampling strategy would you suggest to give the manager the best chance of estimating his customers' satisfaction? Chapter 2, Quiz 1, Form B Page 2 of 4 b) Write a short paragraph for the maids that helps them carry out your method in part (a). Chapter 2, Quiz 1, Form B Page 3 of 4 4. Bias is a serious problem that sometimes arises when one takes a sample. a) In a few sentences, explain generally what bias is. b) What is the distinction between selection bias and non-response bias? Chapter 2, Quiz 1, Form B Page 4 of 4 Chapter 2, Quiz 1, Form B Answer Key 1. Although we may get better information from a census, it is usually far too costly and time consuming to contact every member of the population. A large random sample will be nearly as good for far less cost. 2. A simple random sample of size n is a sample that is selected from a population in a way that ensures that every different possible sample of the desired size has the same chance of being selected. Note: It is important that students not only state that each person has the same chance of being chosen, but also each possible sample of size n has the same chance of being chosen. 3. a) Stratified random sampling. b) Since the manager wants to take noise into account, it would be best to stratify by “rows.” That is, one stratum would be the 12 rooms in building A facing the road, since they are the most similar with regard to noise. The next strata would be the 12 rooms on the other side of building A, etc. Then, in each of the 4 strata, we need to take a random sample of size 3. To do this we can write the 12 room numbers on 12 sheets of paper, mix them up in a hat, and choose three for each strata. 4. a) Bias is the tendency for a sample to differ from the corresponding population in some systematic way. b) Selection bias occurs when some part of the population is systematically excluded from the sample. However, non-response bias occurs when responses are not actually obtained from the individuals who were selected for the sample. Chapter 2, Quiz 1, Form B Answer Key Page 1 of 1 Chapter 2: Collecting Data Section 2.3-2.4 Name ___________________________ 1. We have distinguished two types of studies: observational and experimental. Briefly explain the essential difference(s) between these two types of study. 2. In evaluating an experiment, how would you determine if a variable is an explanatory variable or an extraneous variable? Chapter 2, Quiz 2, Form A Page 1 of 3 3. Suppose that two experiments were conducted to assess the effect of a new insect repellant. In Experiment A, a simple random sample was taken from the population of River City. In Experiment B, a simple random sample from a group of volunteers from the population of River City was used. The results of the experiments were the same: fewer insects landed on the arms that had been treated with the insect repellant. The volunteers were randomly assigned to the two treatments in both experiments. a) For each experiment, A and B, discuss whether one can legitimately infer a cause- and-effect relation between the use of the repellant and fewer insects landing from each of these experiments? Why or why not? b) For each experiment, A and B, discuss whether one can legitimately generalize to the population of River City from each of these experiments? Why or why not? Chapter 2, Quiz 2, Form A Page 2 of 3 4. One of the tasks of wildlife biologists is to estimate bird populations. One method for doing this is to walk a “transect,” typically a long randomly selected rectangle, and count the number of particular species that are seen. During hunting season the biologists wear brightly colored clothes as a protective measure. A theory, known as the “species-confidence hypothesis,” predicts that birds may react to these brightly colored clothes. A robin, for example, when confronted with a biologist wearing an orange color may be less afraid than if the biologist were wearing a brown color. The idea is that the orange color gives the robin some “confidence” that the biologist is another (really big!) bird. This is a difficulty because a robin that is less afraid of the biologist may be easier to see and therefore “count” because the robin lets the biologist get closer. This would result in too high an estimate of the robin population. To test this theory a biologist performed a study in her area, wearing a bright orange vest or a brown vest while working. After training herself to accurately estimate distances she indicated on her notes how close the robins would let her get before they flew away (the “approach distance”), using this as a measure of their “confidence.” She randomly selected her starting points in each trip through the transects and also carefully noted the weather conditions, specifically the wind speed. (a) What is the explanatory variable (factor) for this experiment? (b) What is the response variable for this experiment? (c) After completing the study the biologist was examining her results and noticed that on those days she wore the brightly-colored vest the wind tended to be of greater velocity. How does this information affect the interpretation of the results of the experiment? Chapter 2, Quiz 2, Form A Page 3 of 3 Chapter 2, Quiz 2, Form A Answer Key 1. 2. In an experiment, researchers observe how a response variable behaves when they manipulate one or more factors. However, in an observational study, the researchers do not manipulate any factors. Instead, they observe characteristics of a subset of the members of one or more existing populations. In an experiment, the explanatory variable is the one that researchers manipulate in order to observe changes in the response variable. An extraneous variable is any other variable which is thought to affect the response variable, but is not of interest in the study. 3. a) b) 4. (a) (b) (c) In each of these experiments we can infer a cause-and-effect relationship because the volunteers were randomly assigned to the two treatments. In experiment A, we can generalize the results of the experiment to the population of River City since the subjects were randomly selected from the population of River City. Thus, the subjects should be representative of the population in general. However, in experiment B, the random sample came from a group of volunteers from River City, who may not be representative of the general population of River City. The explanatory variable is the coloration of the vest (bright vs. drab). The response variable is the “approach distance.” The wind velocity is a potential confounding variable. On a windy day the birds may not detect the researcher as easily, or they may be more hesitant to fly. Thus it might be that the results are at least partly the result of wind velocity, not the choice of garment color. Chapter 2, Quiz 2, Form A Answer Key Page 1 of 1