Social life A question posted on the gamefaqs.com website on August 1, 2011, asked

Various claims are often made for surveys. Why is each of the following claims not correct? a) It is always better to take a census than to draw a sample. b) Stopping students on their way out of the cafeteria is a good way to sample if we want to know about the quality of the food there. c) We drew a sample of 100 from the 3000 students in a school. To get the same level of precision for a town of 30,000 residents, well need a sample of 1000. d) A poll taken at a statistics support website garnered 12,357 responses. The majority said they enjoy doing statistics homework. With a sample size that large, we can be pretty sure that most Statistics students feel this way, too. e) The true percentage of all Statistics students who enjoy the homework is called a population statistic.

We need to survey a random sample of the 300 passengers on a flight from San Francisco to Tokyo. Name each sampling method described below. a) Pick every 10th passenger as people board the plane, starting with a randomly chosen passenger among the first 10. b) From the boarding list, randomly choose 5 people flying first class and 25 of the other passengers. c) Randomly generate 30 seat numbers and survey the passengers who sit there. d) Randomly select a seat position (right window, right center, right aisle, etc.) and survey all the passengers sitting in those seats.

Emoticons The website www.gamefaqs.com asked, as their question of the day to which visitors to the site were invited to respond, Do you ever use emoticons when you type online? Of the 87,262 respondents, 27% said that they did not use emoticons. ;-( a) What kind of sample was this? b) How much confidence would you place in using 27% as an estimate of the fraction of people who use emoticons?

Drug tests Major League Baseball tests players to see whether they are using performance-enhancing drugs. Officials select a team at random, and a drug-testing crew shows up unannounced to test all 40 players on the team. Each testing day can be considered a study of drug use in Major League Baseball. a) What kind of sample is this? b) Is that choice appropriate?

Gallup At its website (www.gallup.com) the Gallup Poll publishes results of a new survey each day. Scroll down to the end, and youll find a statement that includes words such as these: Results are based on telephone interviews with 1,008 national adults, aged 18 and older, conducted January 35, 2013. . . . In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls. a) For this survey, identify the population of interest. b) Gallup performs its surveys by phoning numbers generated at random by a computer program. What is the sampling frame? c) What problems, if any, would you be concerned about in matching the sampling frame with the population?

Gallup World At its website (www.gallupworldpoll .com) the Gallup World Poll describes their methods. After one report they explained:

Medical treatments Consumers Union, in an attempt to get information about U.S. adults, asked all subscribers whether they had used alternative medical treatments and, if so, whether they had benefited from them. For almost all of the treatments, approximately 20% of those responding reported cures or substantial improvement in their condition. They received replies from 12% of their subscribers

Snack foods A company packaging snack foods maintains quality control by randomly selecting 10 cases from each days production and weighing the bags. Then they open one bag from each case and inspect the contents. For this exercise, answer the questions both for the bags that are weighed and for the bags that are opened for inspection.

Drinking and driving In order to determine how adults of legal drinking age in their city feel about whether drinking and driving was a problem, researchers waited outside a bar they had randomly selected from a list of such establishments. They rolled a ten-sided die and it came up 4, so they stopped the fourth person who came out of the bar, then every 10th person after that, and asked whether he or she thought drinking and driving was a serious problem.

Mayoral race Hoping to learn what issues may resonate with voters in the coming election, the campaign director for a mayoral candidate randomly selects two blocks from each of the citys election districts. Staff members go there and interview all the residents they can find. The residents were asked to select the three most important issues from a prepared list.

Toxic waste The Environmental Protection Agency took a map of a region near a former industrial waste dump and placed a grid of 552 squares on it. They randomly selected any 16 of those squares from which to collect soil samples and checked each for evidence of toxic chemicals. a) What type of sampling did they use? b) Is there any sort of bias associated with this sampling procedure? c) One researcher suggests that plots closer to the old dump site could contain more contaminants than those farther away. How could the sampling procedure be improved to take this into account?

Social life A question posted on the gamefaqs.com website on August 1, 2011, asked visitors to the site, Do you have an active social life outside the Internet? 22% of the 55,581 respondents said No or Not really, most of my personal contact is online. a) Can this survey be used to estimate the proportion of U.S. adults who would say they have an active social life outside the Internet? Why or why not? b) Can this survey be used to estimate the proportion of visitors to their site who would say they have an active social life outside the Internet? Why or why not?

Roadblock State police set up a roadblock to estimate the percentage of cars with up-to-date registration, insurance, and safety inspection stickers. It would be too inconvenient and costly to check every vehicle that passes through a checkpoint, so they decide to stop about 1/20 of the vehicles. a) Why would a simple random sample be unreasonable for this situation. b) Identify two possible sampling schemes that could be used. Explain how randomization would be used in each.

Milk samples Dairy inspectors visit farms unannounced and take samples of the milk to test for contamination. If the milk is found to contain dirt, antibiotics, or other foreign matter, the milk will be destroyed and the farm reinspected until purity is restored. Would simple random sampling be appropriate for selecting farms for inspection? If so, explain how it would be done. If not, explain why it is not appropriate.

Mistaken poll A local TV station conducted a PulsePoll about the upcoming mayoral election. Evening news viewers were invited to phone in their votes, with the results to be announced on the late-night news. Based on the phone calls, the station predicted that Amabo would win the election with 52% of the vote. They were wrong: Amabo lost, getting only 46% of the vote. Do you think the stations faulty prediction is more likely to be a result of bias or sampling error? Explain

Another mistaken poll Prior to the mayoral election discussed in Exercise 15, the newspaper also conducted a poll. The paper surveyed a random sample of registered voters stratified by political party, age, sex, and area of residence. This poll predicted that Amabo would win the election with 52% of the vote. The newspaper was wrong: Amabo lost, getting only 46% of the vote. Do you think the newspapers faulty prediction is more likely to be a result of bias or sampling error? Explain.

Parent opinion, part 1 In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. a) Put a big ad in the newspaper asking people to log their opinions on the PTA website. b) Randomly select one of the elementary schools and contact every parent by phone. c) Send a survey home with every student, and ask parents to fill it out and return it the next day. d) Randomly select 20 parents from each elementary school. Send them a survey, and follow up with a phone call if they do not return the survey within a week.

Parent opinion, part 2 Lets revisit the school system described in Exercise 17. Four new sampling strategies have been proposed to help the PTA determine whether parents favor requiring elementary students to pass a test in order to be promoted to the next grade. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. a) Run a poll on the local TV news, asking people to dial one of two phone numbers to indicate whether they favor or oppose the plan. b) Hold a PTA meeting at each of the 20 elementary schools, and tally the opinions expressed by those who attend the meetings. c) Randomly select one class at each elementary school and contact each of those parents. d) Go through the districts enrollment records, selecting every 40th parent. PTA volunteers will go to those homes to interview the people chosen.

Churches For your political science class, youd like to take a survey from a sample of all the Catholic Church members in your city. A list of churches shows 17 Catholic churches within the city limits. Rather than try to obtain a list of all members of all these churches, you decide to pick 3 churches at random. For those churches, youll ask to get a list of all current members and contact any 100 members selected at random. a) What kind of design have you used? b) What could go wrong with your design?

Playground Some people have been complaining that the childrens playground at a municipal park is too small and is in need of repair. Managers of the park decide to survey city residents to see if they believe the playground should be rebuilt. They hand out questionnaires to parents who bring children to the park. Describe possible biases in this sample

oller coasters An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to 3 hours for a 2-minute ride. Concerned about how patrons (who paid a large amount to enter the park and ride on the rides) feel about this, they survey every 10th person on the line for the roller coaster, starting from a randomly selected individual. a) What kind of sample is this? b) What is the sampling frame? c) Is it likely to be representative?

Playground, act two The survey described in Exercise 20 asked, Many people believe this playground is too small and in need of repair. Do you think the playground should be repaired and expanded even if that means raising the entrance fee to the park? Describe two ways this question may lead to response bias.

Wording the survey Two members of the PTA committee in Exercises 17 and 18 have proposed different questions to ask in seeking parents opinions. Question 1: Should elementary schoolage children have to pass high-stakes tests in order to remain with their classmates? Question 2: Should schools and students be held accountable for meeting yearly learning goals by testing students before they advance to the next grade? a) Do you think responses to these two questions might differ? How? What kind of bias is this? b) Propose a question with more neutral wording that might better assess parental opinion.

Banning ephedra An online poll at a website asked: A nationwide ban of the diet supplement ephedra went into effect recently. The herbal stimulant has been linked to 155 deaths and many more heart attacks and strokes. Ephedra manufacturer NVE Pharmaceuticals, claiming that the FDA lacked proof that ephedra is dangerous if used as directed, was denied a temporary restraining order on the ban yesterday by a federal judge. Do you think that ephedra should continue to be banned nationwide? 65% of 17,303 respondents said yes. Comment on each of the following statements about this poll: a) With a sample size that large, we can be pretty certain we know the true proportion of Americans who think ephedra should be banned. b) The wording of the question is clearly very biased. c) The sampling frame is all Internet users. d) Results of this voluntary response survey cant be reliably generalized to any population of interest.

Survey questions Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question. a) Should companies that pollute the environment be compelled to pay the costs of cleanup? b) Given that 18-year-olds are old enough to vote and to serve in the military, is it fair to set the drinking age at 21?

. More survey questions Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question. a) Do you think high school students should be required to wear uniforms? b) Given humanitys great tradition of exploration, do you favor continued funding for space flights?

Phone surveys Anytime we conduct a survey, we must take care to avoid undercoverage. Suppose we plan to select 500 names from the city phone book, call their homes between noon and 4 pm, and interview whoever answers, anticipating contacts with at least 200 people. a) Why is it difficult to use a simple random sample here? b) Describe a more convenient, but still random, sampling strategy. c) What kinds of households are likely to be included in the eventual sample of opinion? Excluded? d) Suppose, instead, that we continue calling each number, perhaps in the morning or evening, until an adult is contacted and interviewed. How does this improve the sampling design? e) Random-digit dialing machines can generate the phone calls for us. How would this improve our design? Is anyone still excluded?

Cell phone survey What about drawing a random sample only from cell phone exchanges? Discuss the advantages and disadvantages of such a sampling method compared with surveying randomly generated telephone numbers from noncell phone exchanges. Do you think these advantages and disadvantages have changed over time? How do you expect theyll change in the future?

Arm length How long is your arm compared with your hand size? Put your right thumb at your left shoulder bone, stretch your hand open wide, and extend your hand down your arm. Put your thumb at the place where your little finger is, and extend down the arm again. Repeat this a third time. Now your little finger will probably have reached the back of your left hand. If the fourth hand width goes past the end of your middle finger, turn your hand sideways and count finger widths to get there. a) How many hand and finger widths is your arm? b) Suppose you repeat your measurement 10 times and average your results. What parameter would this average estimate? What is the population? c) Suppose you now collect arm lengths measured in this way from 9 friends and average these 10 measurements. What is the population now? What parameter would this average estimate? d) Do you think these 10 arm lengths are likely to be representative of the population of arm lengths in your community? In the country? Why or why not?

Fuel economy Occasionally, when I fill my car with gas, I figure out how many miles per gallon my car got. I wrote down those results after 6 fill-ups in the past few months. Overall, it appears my car gets 28.8 miles per gallon. a) What statistic have I calculated? b) What is the parameter Im trying to estimate? c) How might my results be biased? d) When the Environmental Protection Agency (EPA) checks a car like mine to predict its fuel economy, what parameter is it trying to estimate?

Accounting Between quarterly audits, a company likes to check on its accounting procedures to address any problems before they become serious. The accounting staff processes payments on about 120 orders each day. The next day, the supervisor rechecks 10 of the transactions to be sure they were processed properly. a) Propose a sampling strategy for the supervisor. b) How would you modify that strategy if the company makes both wholesale and retail sales, requiring different bookkeeping procedures?

Happy workers? A manufacturing company employs 14 project managers, 48 foremen, and 377 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a sample of employees every month. a) Do you see any potential danger in the companys plan? Explain. b) Propose a sampling strategy that uses a simple random sample. c) Why do you think a simple random sample might not provide the representative opinion the company seeks?d) Propose a better sampling strategy. e) Listed below are the last names of the project managers. Use random numbers to select two people to be interviewed. Explain your method carefully.

Quality control Sammys Salsa, a small local company, produces 20 cases of salsa a day. Each case contains 12 jars and is imprinted with a code indicating the date and batch number. To help maintain consistency, at the end of each day, Sammy selects three jars of salsa, weighs the contents, and tastes the product. Help Sammy select the sample jars. Todays cases are coded 07N61 through 07N80. a) Carefully explain your sampling strategy. b) Show how to use random numbers to pick 3 jars. c) Did you get a simple random sample of the jars? Explain.

A fish story Concerned about reports of discolored scales on fish caught downstream from a newly sited chemical plant, scientists set up a field station in a shoreline public park. For one week they asked fishermen there to bring any fish they caught to the field station for a brief inspection. At the end of the week, the scientists said that 18% of the 234 fish that were submitted for inspection displayed the discoloration. From this information, can the researchers estimate what proportion of fish in the river have discolored scales? Explain.

Sampling methods Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. a) We want to know what percentage of local doctors accept Medicaid patients. We call the offices of 50 doctors randomly selected from local Yellow Page listings. b) We want to know what percentage of local businesses anticipate hiring additional employees in the upcoming month. We randomly select a page in the Yellow Pages and call every business listed there.

More sampling methods Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. a) We want to know if there is neighborhood support to turn a vacant lot into a playground. We spend a Saturday afternoon going door-to-door in the neighborhood, asking people to sign a petition. b) We want to know if students at our college are satisfied with the selection of food available on campus. We go to the largest cafeteria and interview every 10th person in line.

Texas A&M Administrators at Texas A&M University were interested in estimating the percentage of students who are the first in their family to go to college. The A&M student body has about 46,000 members. a) What problems do you see with asking the following question of students? Are you the first member of your family to seek higher education? b) For each scenario, identify the kind of sample used by the university administrators: i. Select several dormitories at random and contact everyone living in the selected dorms. ii. Using a computer-based list of registered students, contact 200 freshmen, 200 sophomores, 200 juniors, and 200 seniors selected at random from each class. iii. Using a computer-based alphabetical list of registered students, select one of the first 25 on the list by random and then contact the student whose name is 50 names later, and then every 50 names beyond that. c) A professor teaching a large lecture class of 350 students samples her class by rolling a die. Then, starting with the row number on the die (1 to 6), she passes out a survey to every fourth row of the large lecture hall. She says that this is a Simple Random Sample because everyone had an equal opportunity to sit in any seat and because she randomized the choice of rows. What do you think? Be specific. d) For each of these proposed survey designs, identify the problem and the effect it would have on the estimate of the percentage of students who are the first in their family to go to college. i. Publish an advertisement inviting students to visit a website and answer questions. ii. Set up a table in the student union and ask students to stop and answer a survey. e) The president of the university plans a speech to an alumni group. He plans to talk about the proportion of students who responded in the survey that they are the first in their family to attend college, but the first draft of his speech treats that proportion as the actual proportion of current A&M students who are the first in their families to attend college. Explain to the president the difference between the proportion of respondents who are first attenders and the proportion of the entire student body that are first attenders. Use appropriate statistics terminology.

Satisfied workers The managers of a large company wished to know the percentage of employees who feel extremely satisfied to work there. The company has roughly 24,000 employees. They contacted a random sample of employees and asked them about their job satisfaction, obtaining 437 completed responses. a) The companys annual report states, Our survey shows that 87.34% of our employees are very happy working here. Comment on that claim. Use appropriate statistics terminology. b) One manager suggested surveying employees by assigning computer-generated random numbers to each employee on a list of all employees and then contacting all those whose assigned random number is divisible by 7. Is this a simple random sample? c) For each scenario suggested by a different manager, determine the sampling method. i. Use the company e-mail directory to contact 150 employees from among those employed for less than 5 years, 150 from among those employed for 510 years, and 150 from among those employed for more than 10 years. ii. Use the company e-mail directory to contact every 50th employee on the list. iii. Select several divisions of the company at random. Within each division, draw an SRS of employees to contact. d) One manager suggested having the head of each corporate division hold a meeting of their employees to ask whether they are happy on their jobs. They will ask people to raise their hands to indicate whether they are happy. What problems do you see with this plan? e) For each of these designs proposed by a different manager, identify the problem with the method and the effect it would have on the estimate of the percentage of employees who feel extremely satisfied to work there. i. Leave a stack of surveys out in the employee cafeteria so people can pick them up and return them. ii. Stuff a questionnaire in the mailbox of each employee with the request that they fill it out and return it.