Quiz 4.1AAP Statisticsname

Quiz 4.1AAP StatisticsName:

For each of the following situations involving sampling, identify—as precisely as possible— the population that the sample represents.

(a)A business school researcher wants to know what factors affect the survival and success of small businesses. She selects a sample of 150 eating-and-drinking establishments from those listed in the telephone directory for a large city.

(b)A member of Congress wants to know whether his constituents support proposed legislation on health care. His staff reports that 228 letters have been received on the subject, of which 193 oppose the legislation.

A local radio talk-show host asks viewers to call in and vote for or against a proposed plan to raise the prices charged by municipal parking meters in a downtown shopping district. 75% of the respondents are opposed to the increase. Describe one possible source of error or bias that might arise in this poll and indicate the direction in which the estimate might be biased. What is the name for this kind of bias?

Two different organizations conduct polls in a city whose mayor has been accused of taking bribes. One poll asks a SRS of city residents, ―Do you think the mayor should resign because of accusations of his criminal activity?‖ The other asks, ―Do you think the mayor should resign?‖ The first poll concluded that the majority of city residents think the mayor should resign. The second poll drew exactly the opposite conclusion. Explain why their results might be so different.

Your school will send a delegation of 35 seniors to a student life convention. 200 girls and 150 boys are eligible to be chosen. If a sample of 20 girls and separate sample 15 boys are each selected randomly, it gives each senior the same chance to be chosen to attend the convention.

(a) Is it an SRS? Explain.

(b)Beginning at line 108 in the random digits table, reproduced below, select the first three senior girls to be in the sample. Explain your procedures clearly.

108 / 60940 / 72024 / 17868 / 24943 / 61790 / 90656 / 87964
18883
109 / 36009 / 19365 / 15412 / 39638 / 85453 / 46816 / 83485
41979
110 / 38448 / 48789 / 18338 / 24697 / 39364 / 42006 / 76688
08708

Quiz 4.1BAP StatisticsName:

For each of the following situations involving sampling, identify—as precisely as possible— the population that the sample represents.

(a)An insurance company wants to monitor the quality of its procedures for handling loss claims from its auto insurance policyholders. Each month the company selects an SRS of all auto insurance claims filed that month to examine them for accuracy and promptness.

(b)A college admissions officer wants to know what the most important factors are that high school seniors consider when they choose where to apply to college. She conducts a telephone survey with a simple random sample of all applicants to her college.

In late 1995, a Gallup survey reported that about 46% Americans approved of sending troops to Bosnia. The poll did not mention that 20,000 U.S. troops were committed to go. A CBS News poll mentioned the 20,000 figure and got a different outcome—an approval rate of only 33%. Briefly explain why the mention of the number of troops would cause such a big difference in the poll results. Write the name of the kind of bias that is at work here.

A church group interested in promoting volunteerism in a community chooses an SRS of 200 community addresses and sends members to visit these addresses during weekday working hours to inquire about the residents’ attitudes toward volunteer work. Sixty percent of all respondents say that they would be willing to donate at least an hour a week to some volunteer organization. Bias is present in this sample design. Identify the type of bias involved and state whether you think the sample percent obtained is higher or lower than the true population percent.

Each state conducts an annual study of seat belt use by drivers following guidelines set by the federal government. Seat belt use is observed at randomly chosen road locations at random times during daylight hours. The locations are based on counties within each state. In

Hawaii, the counties are the islands that make up the state’s territory, and the survey is conducted on the 4 most populated islands: Oahu, Maui, Hawaii (referred to as ―The Big

Island‖), and Kauai. The sample sizes on the islands are proportional to the amount of road traffic., so each location is equally likely to be selected.

(a)Is this a SRS of road locations in the state of Hawaii? Explain.

(b) Suppose there are 476 possible road locations on Kauai and we need to randomly select 22 of them to be in the sample. Beginning at line 120 in the random digits table below, choose the first 3 road locations for the seat belt survey sample. Explain your method clearly.

12035476 55972 39421 65850 04266 35435 43742 11937

12171487 09984 29077 14863 61683 47052 62224 51025

12213873 81598 95052 90908 73592 75186 87136 95761

Quiz 4.1CAP StatisticsName:

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.

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.

135 66925 55658 39100 78458 11206 19876 87151 31260

136 08421 44753 77377 28744 75592 08563 79140 92454

137 53645 66812 61421 47836 12609 15373 98481 14592

Quiz 4.2AAP StatisticsName:

A medical study of heart surgery investigates the effect of a drug called a beta-blocker on the pulse rate of the patient during surgery. The pulse rate will be measured at a specific point during the operation. The investigators will use 20 patients facing heart surgery as subjects. You have a list of these patients, numbered 1 to 20, in alphabetical order.

Describe the design of a completely randomized, controlled experiment to test the effect of beta-blockers on pulse rate during surgery.

Use the section from the random digits table below to carry out the randomization required by your design and list the outcome of the randomization.

96746 / 12149 / 37823 / 71868 / 18442 / 35119 / 62103 / 39244
96927 / 19931 / 36809 / 74192 / 77567 / 88741 / 48409 / 41903
43909 / 99477 / 25330 / 64359 / 40085 / 16925 / 85117 / 36071
15689 / 14227 / 06565 / 14374 / 13352 / 49367 / 81982 / 87209
36759 / 58984 / 68288 / 22913 / 18638 / 54303 / 00795 / 08727

A family restaurant chain wants to test the market for a new menu item: a grilled chicken sandwich with chipotle salsa. They are interested in both how to market the item and the

right price to charge for it. They decide to offer the sandwich at 60 different restaurants in the chain, using two different descriptions on the menu. Half the restaurants’ menus will emphasize ―healthy eating‖ and half will emphasize ―value.‖ These two groups of restaurants will be further divided in three groups, each charging either a High, Medium, or Low price for the sandwich. After a month, they will measure what proportion of customers order the new sandwich.

(a)Suppose the company plans to conduct a completely randomized design. List the experimental units, factors, and treatments in this experimental design.

(b)Suppose that 30 of the restaurants in the study are free-standing buildings and the other 30 are located inside malls. The company suspects that the different building types may have impact on how people respond to the advertising campaign and the price. How might they alter the design of this experiment to take this into account?

A college fitness center offers an exercise program for staff members who choose to participate. The program assesses each participant’s fitness using a treadmill test, and also administers a personality questionnaire. There is a moderately strong positive correlation between fitness score and score for self-confidence. Explain why it would not be possible to conclude from this study that the exercise program increases one’s self-confidence.

Quiz 4.2BAP StatisticsName:

Agricultural scientists for a chemical company want to determine if a newly developed fertilizer produces heavier tomatoes than the fertilizer they currently manufacture. For their first pilot study, they have 24 healthy young tomato plants growing in individual pots, numbered from 1 to 24.

Describe the design of a completely randomized, controlled experiment to test the whether the new fertilizer produces heavier tomatoes.

Use the section from the random digits table below to carry out the randomization required by your design and list the outcome of the randomization.

27816 78416 18329 21337 35213 37741 04312 68508

66925 55658 39100 78458 11206 19876 87151 31260

08421 44753 77377 28744 75592 08563 79140 92454

53645 66812 61421 47836 12609 15373 98481 14592

66831 68908 40772 21558 47781 33586 79177 06928

The customer service call center for a major electronics manufacturer is trying to determine how to keep customers who are on hold as happy as possible. They want to examine whether the type of music they play while customers are on hold and whether or not there is a periodically-repeated recorded message (―Thank you for you patience, we’ll be with you as soon as possible.‖) have an impact on customer satisfaction. They plan to randomly select customers who are on hold and play one of three different types of music (―smooth‖ jazz, classical, or Broadway show tunes) and either play recorded messages or not. After the entire call is over, they will ask the customers to rate their overall customer service experience.

(a)Suppose the company plans to conduct a completely randomized design. List the experimental units, factors and treatments in this experimental design.

(b)Suppose the company is concerned that the time when the call is made (daytime versus evening) will have an impact on which combination of music and messages is most effective. How might they alter the design of this experiment to take this into account?

Many utility companies have introduced programs to encourage energy conservation among their customers. An electric company considers placing electronic meters in households to show what the cost would be if the electricity use at that moment continued for a month. It gives these meters to 100 of its customers for a year and then compares the average electricity use in these customers’ homes this year to the previous year. Result: These customers’ average electricity use decreased by 10%. Explain why this is not strong evidence that the use of the electronic meters caused customers to decrease their electricity use.

Quiz 4.2CAP StatisticsName:

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 children.

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 Fº) and high (75 Fº) temperatures and two types of packaging—plastic and waxed cardboard. List the experimental units, factors, and treatments in this experiment.

An experiment to investigate the effectiveness of white-willow-bark capsules as a remedy for back pain plans to compare the reduction in pain for people using this herbal remedy to a control group. Is it possible to conduct this experiment in a double-blind? Explain.

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:

Section / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8
Lecturer / Hilton / Christensen / Hadfield / Hadfield / Tolley / Hilton / Tolley / Christensen

(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.

Quiz 4.3AAP StatisticsName:

1.For each study described below, comment on the extent to which inferences can be drawn about a larger population and whether cause and effect can be established. .

(a)A football coach thinks lessons in yoga will improve the flexibility of his players and thereby reduce injuries. To test his theory, he randomly divides the players on the team into two groups. One group has 45 minutes of yoga training each day. The players in the other group do the standard stretching routine the team has used in the past. He compares flexibility in the two groups at the end of the experiment.

(b)Does lack of sleep affect your academic performance? A student explores this question by asking everyone in his statistics class to write down on a piece of paper his or her score on a recent test and total number of hours of sleep he or she got on the last three nights before taking the test.

(c)Does ―Cold-Cut,‖ a popular over-the-counter cold remedy that claims to reduce the length and severity of colds really work? A consumer advocacy group addresses this question by asking a random sample of 400 adults how many colds they’d had in the last six months, how long each cold lasted, and if they took ―Cold-Cut‖ to treat the cold.

Preliminary observational studies have linked consumption of caffeine during pregnancy to a higher incidence of miscarriages. It would be unethical to run a controlled experiment to establish cause and effect in this situation. Describe two ways in which researchers can seek to establish cause and effect that do not involve experiments.

Quiz 4.3BAP StatisticsName:

For each study described below, comment on the extent to which inferences can be drawn about a larger population and whether cause and effect can be established.

(a)A teacher wants to decide if handing out a topic outline before the final exam improves the exam scores of calculus students. He has two sections of calculus this term. His gives one class a topic outline and tell the other class to generate their own topic outline.

He then compares the two sections’ scores on the final exam.

(b)Does blood type determine your personality? In a study aimed at answering this question, a random sample of 100 adults were given a personality test, and a comparison was made between the scores on the introversion/extroversion scale and blood type (A, B, AB, O).

(c)Does using a calculator improve understanding of mathematical concepts? All 200 fifth-graders at a school are randomly assigned to one of two groups. One group studies addition of fractions with the aid of a calculator, the other studies the same topic without a calculator. Scores on a fractions test are compared after two weeks.

A few studies have suggested that people who live within a few hundred yards of high-voltage power lines are more likely to get certain forms of cancer. It would be both unethical and impractical to conduct a controlled experiment to establish cause and effect in this situation. Describe two ways in which researchers can seek to establish cause and effect that do not involve experiments.

Quiz 4.3CAP StatisticsName:

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.