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Name: _______________________________________________ Per: ____ Date: ______________Chapter 4 Problem Set A.P. Statistics1) A university’s financial aid office wants to know how much it can expect students to earn from summer employment. This information will be used to set the level of financial aid. The population contains 3478 students who have completed at least one year of study but have not yet graduated. A questionnaire will be sent to an SRS of 100 of these students, drawn from an alphabetized list. (a) Describe how you will select the sample. (b) Starting at line 135, use the portion of the random digits table below to select the first three students in the sample. 13566925 55658 39100 78458 11206 19876 87151 31260 13608421 44753 77377 28744 75592 08563 79140 92454 13753645 66812 61421 47836 12609 15373 98481 145922) The school’s newspaper has asked you to contact 100 of the approximately 1100 students at the school to gather information about student opinions regarding food at your school’s cafeteria. (a) With as much precision as possible, describe the population for your study. (b) You are pretty sure that there is a big difference between the opinions of males and females when it comes to cafeteria food. Describe a study design that takes into account this potentially important variable. Explain the advantage of this method. (c) You decide to conduct a survey about the quality of food served in the school cafeteria by randomly selecting students as they leave the cafeteria after lunch on a specific day next week. Describe a source of bias that may result from using this method. Be sure to use the correct terminology, and indicate the direction of the potential bias.3) An article in a women’s magazine says that women who choose to nurse their babies feel warmer and more receptive toward the infants than mothers who bottle-feed. The author concludes that nursing has desirable effects on the mother’s attitude toward the child. Explain why asserting a causal relationship based on this information is suspect, and give another plausible explanation for the association between the decision to bottle-feed or nurse and mothers’ attitudes toward their children4) A cookie manufacturer is trying to determine how long cookies stay fresh on store shelves, and the extent to which the type of packaging and the store’s temperature influences how long the cookies stay fresh. He designs a completely randomized experiment involving low (64 F?) and high (75 F?) temperatures and two types of packaging—plastic and waxed cardboard. List the experimental units, factors, and treatments in this experiment.5) The Brigham Young University statistics department is conducting a series of randomized comparative experiments to compare teaching methods. Response variables include students’ final-exam scores and a measure of their attitude toward statistics. One study compares two levels of technology for large-group lectures: standard (overhead projectors and chalk) and multimedia. The experimental units in the study are the 8 lecture sections in a basic statistics course. There are four instructors, each of whom teaches two sections. Because the lecturers differ, their lectures form four blocks. Suppose the sections and lecturers are as follows:(a) Outline the design of an experiment using blocking to determine which lecture method is most effective. Be sure to explain how you will randomly assign the treatments, using the random digits table below. 71487 09984 29077 14863 61683 47052 62224 51025 13873 81598 95052 90908 73592 75186 87136 95761 54580 81507 27102 56027 55892 33063 41842 81868 71035 09001 43367 49497 72719 96758 27611 91596(b) Explain why a randomized block design is better than a completely randomized design in this case.6) For each study describe below, comment briefly on the extent to which results can be generalized to some larger population, and the extent to which cause and effect has been established. (a) A marketing executive who wants to gauge reactions to a new packaging design for a popular brand of cookie places the new packages in 45 randomly-selected grocery stores in a large city and compares sales of the cookies to sales of the same cookie (with the old packaging) in the previous month. (b) A consumer advocacy organization wants to determine if using premium gasoline in the engines of cars improves gas mileage. They randomly select 40 makes and models of new cars and acquire two of each. They run each car on a track for 1000 miles, one with regular gasoline, one with premium. (Which car within each pair gets the premium gas is determined by coin flip). After driving each car, they determine the difference in fuel consumption within each pair of cars. (c) A high school student thinks that the longer a student has been at the school, the less they like the food in the cafeteria. To test this theory, she gives a two-question survey to the first 100 people who enter the cafeteria on a certain day. The first question is, “How long have you attended school here?” The second question asks the student to rate the food in the cafeteria on a 1 to 5 scale. 7) In response to nutrition concerns raised last year about food served in school cafeterias, the Smallville School District entered into a one-year contract with the Healthy Alternative Meals (HAM) company. Under this contract, the company plans and prepares meals for 2,500 elementary, middle, and high school students, with a focus on good nutrition. The school administration would like to survey the students in the district to estimate the proportion of students who are satisfied with the food under this contract. Two sampling plans for selecting the students to be surveyed are under consideration by the administration. One plan is to take a simple random sample of students in the district and then survey those students. The other plan is to take a stratified random sample of students inthe district and then survey those students. (a) Describe a simple random sampling procedure that the administrators could use to select 200 students from the 2,500 students in the district. (b) If a stratified random sampling procedure is used, give one example of an effective variable on which to stratify in this survey. Explain your reasoning. (c) Describe one statistical advantage of using a stratified random sample over a simple random sample in the context of this study8) Agricultural experts are trying to develop a bird deterrent to reduce costly damage to crops in the United States. An experiment is to be conducted using garlic oil to study its effectiveness as a nontoxic, environmentally safe bird repellant. The experiment will use European starlings, a bird species that causes considerable damage annually to the corn crop in the United States. Food granulesmade from corn are to be infused with garlic oil in each of five concentrations of garlic —0 percent,2 percent, 10 percent, 25 percent, and 50 percent. The researchers will determine the adverse reaction of the birds to the repellantby measuring the number of food granules consumed during a two-hour period following overnight food deprivation. There are forty birds available for the experiment, and the researchers will use eight birds for each concentration of garlic. Each bird will be kept in a separate cage and provided with the same number of food granules. (a) For the experiment, identify i. the treatments ii. the experimental units iii. the response that will be measured (b) After performing the experiment, the researchers recorded the data shown in the table below.Garlic oil concentration 0% 2% 10% 25% 50% Mean number of food granules consumed 58 48 29 24 20 Number of birds 8 8 8 8 8Construct a graph of the data that could be used to investigate the appropriateness of a linear regression model for analyzing the results of the experiment. ii. Based on your graph, do you think a linear regression model is appropriate? Explain.9) Before beginning a unit on frog anatomy, a seventh-grade biology teacher gives each of the 24 students in the class a pretest to assess their knowledge of frog anatomy. The teacher wants to compare the effectiveness of an instructional program in which students physically dissect frogs with the effectiveness of a different program in which students use computer software that only simulates the dissection of a frog. After completing one of the two programs, students will be given a posttest to assess their knowledge of frog anatomy. The teacher will then analyze the changes in the test scores (score on posttest minus score on pretest). (a) Describe a method for assigning the 24 students to two groups of equal size that allows for a statistically valid comparison of the two instructional programs. (b) Suppose the teacher decided to allow the students in the class to select which instructional program on frog anatomy (physical dissection or computer simulation) they prefer to take, and 11 students choose actual dissection and 13 students choose computer simulation. How might that self-selection process jeopardize a statistically valid comparison of the changes in the test scores (score on posttest minus score on pretest) for the two instructional programs? Provide a specific example to support your answer.10) A local school board plans to conduct a survey of parents’ opinions about year-round schooling in elementary schools. The school board obtains a list of all families in the district with at least one child in an elementary school and sends the survey to a random sample of 500 of the families. The survey question is provided below. A proposal has been submitted that would require students in elementary schools to attend school on a year round basis. Do you support this proposal? (Yes or No) The school board received responses from 98 of the families, with 76 of the responses indicating support for year-round schools. Based on this outcome, the local school board concludes that most of the families with at least one child in elementary school prefer year-round schooling. (a) What is a possible consequence of nonresponse bias for interpreting the results of this survey? (b) Someone advised the local school board to take an additional random sample of 500 families and to use the combinedresults to make their decision. Would this be a suitable solution to the issue raised in part (a)? Explain.(c) Suggest a different follow-up step from the one suggested in part (b) that the local school board could take to address the issue raised in part (a). ................
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