Find the margin of error Example 5.12 tells us that Gallup

Instant opinion A recent online poll posed the question: Should female athletes be paid the same as men for the work they do? In all, 13,147 (44%) said Yes, another 15,182 (50%) said No, and the remaining 1448 said Dont know. (a) What is the sample size for this poll? (b) Th ats a much larger sample than standard sample surveys. In spite of this, we cant trust the result to give good information about any clearly defi ned population. Why?

An online poll In June 2008, Parade magazine posed the following question: Should drivers be banned from using all cell phones? Readers were encouraged to vote online at parade.com. Th e July 13, 2008, issue of Parade reported the results: 2407 (85%) said Yes and 410 (15%) said No. (a) What type of sample did the Parade survey obtain? (b) Explain why this sampling method is biased. Is 85% probably higher or lower than the true percent of all adults who believe that cell phone use while driving should be banned? Why?

Sleepless nights How much sleep do high school students get on a typical school night? An interested student designed a survey to fi nd out. To make data collection easier, the student surveyed the fi rst 100 students to arrive at school on a particular morning. Th ese students reported an average of 7.2 hours of sleep on the previous night. (a) What type of sample did the student obtain? (b) Explain why this sampling method is biased. Is 7.2 hours probably higher or lower than the true average amount of sleep last night for all students at the school? Why?

Hand-washing habits Do adults typically wash their hands aft er using the bathroom? In a telephone survey of 1001 U.S. adults, 92% said they always wash their hands aft er using a public restroom.2 An observational study of 6076 adults in public restrooms told a slightly diff erent story: only 77% of those observed actually washed their hands aft er using the restroom.3 (a) Why do you think the results of the two studies are so diff erent? (b) According to a description of the observational study, Observers discreetly watched and recorded whether or not adults using public restrooms washed their hands. Observers were instructed to groom themselves (comb their hair, put on make-up, etc.) while observing and to rotate bathrooms every hour or so to avoid counting repeat users more than once. Observers were also instructed to wash their hands no more than 10 percent of the time. Explain why these precautions were taken by the observers.

Design your own bad sample A large high school wants to gather student opinion about parking for students on campus. It isnt practical to contact all students. (a) Give an example of a way to choose a sample of students that is bad because it depends on voluntary response. (b) Give another example of a bad way to choose a samplebut this time one that doesnt use voluntary response.

More capture-recapture Refer to Activity 5.1A (page 202). Mr. Washingtons class takes an initial sample of 50 goldfi sh. Aft er replacing the 50 tagged fi sh, the class obtains a second sample of fi sh. Of the 75 fi sh in this sample, 25 of the tagged fi sh are recaptured (along with 50 untagged fi sh). (a) Compute an estimate of the total number of fi sh in the lake. Show your method clearly. (b) Is the number of fi sh you calculated in (a) defi nitely, probably, probably not, or defi nitely not equal to the actual number of fi sh in the lake? Why? (c) Explain why the capture-recapture sampling method used in this Activity is not biased.

Apartment living You are planning a report on apartment living in a college town. You decide to select three apartment complexes at random for in-depth interviews with residents. Use Table B, starting at line 117, to select a simple random sample of three of the following apartment complexes. Explain your method clearly enough for a classmate to obtain your results. Ashley Oaks Country View Mayfair Village Bay Pointe Country Villa Nobb Hill Beau Jardin Crestview Pemberly Courts Bluff s Del-Lynn Peppermill Brandon Place Fairington Pheasant Run Briarwood Fairway Knolls Richfi eld Brownstone Fowler Sagamore Ridge Burberry Franklin Park Salem Courthouse Cambridge Georgetown Village Manor Chauncey Village Greenacres Waterford Court Country Squire Lahr House Williamsburg

How do random digits behave? Which of the following statements are true of a table of random digits, and which are false? Explain your answers. (a) Th ere are exactly four 0s in each row of 40 digits. (b) Each pair of digits has chance 1/100 of being 00. (c) Th e digits 0000 can never appear as a group, because this pattern is not random.

An election day sample You want to choose an SRS of 25 of a citys 440 voting precincts for special voting-fraud surveillance on election day. (a) Explain clearly how you would label the 440 precincts. How many digits make up each of your labels? What is the greatest number of precincts you could label using this number of digits? (b) Use Table B at line 107 to choose the fi rst 10 precincts in the SRS.

Is this an SRS? A university has 1000 male and 500 female faculty members. A survey of faculty opinion selects 100 of the 1000 men at random and then separately selects 50 of the 500 women at random. Th e 150 faculty members chosen make up the sample. (a) Explain why this sampling method gives each member of the faculty an equal chance to be chosen. (b) Nonetheless, this is not an SRS. Why not?

Drug testing Use the table of random digits (Table B) to select an SRS of 3 of the following 25 members of an athletic team for a drug test. Be sure to say where you entered the table and how you used it. Agarwal Fuest Milhalko Shen Andrews Fuhrmann Moser Smith Baer Garcia Musselman Sundheim Berger Healy Pavnica Wilson Brockman Hixson Petrucelli Chen Lee Reda Frank Lynch Roberts

Not an SRS Its sometimes not practical to take a simple random sample. Heres an example that shows why. Suppose 1000 iPhones are produced at a factory today. Management would like to ensure that the phones display screens meet their quality control standards before shipping them to retail stores. Since it takes about 10 minutes to inspect an individual phones display screen, managers decide to inspect a sample of 20 phones from the days production. (a) Explain why it would be diffi cult for managers to inspect an SRS of 20 iPhones that are produced today. (b) An eager employee suggests that it would be easy to inspect the last 20 iPhones that were produced today. Why isnt this a good idea? (c) Another employee recommends inspecting every fi ft ieth iPhone that is produced. Explain carefully why this sampling method is not an SRS.

SRS applet Explain how you would use the Simple Random Sample applet from Activity 5.1B (page 211) to perform each of the following tasks. Try each of your ideas to be sure that it works. Can the applet be used in more than one way to carry out any of these tasks? Explain. (a) Flip a coin. (b) Shuffl e a deck of 52 cards. (c) Pick a jury of 12 people from a small town with a population of 500 adult citizens.

SRS on the calculator Explain how you would use your calculators randInt command to perform each of the tasks in Exercise 5.13, if possible. Try each of your ideas to be sure that it works.

Rating the police Th e Miami Police Department wants to know how black residents of Miami feel about police service. A researcher prepares several questions about the police. Th e police department chooses an SRS of 300 mailing addresses in predominantly black neighborhoods and sends a uniformed black police offi cer to each address to ask the questions of an adult living there. (a) What are the population and the sample? (b) Why are the results likely to be biased even though the sample is an SRS?

A call-in opinion poll Should the United Nations continue to have its headquarters in the United States? A television program asked its viewers to call in with their opinions on that question. Th ere were 186,000 callers, 67% of whom said No. A nationwide random sample of 500 adults found that 72% answered Yes to the same question.5 Explain to someone who knows no statistics why the opinions of only 500 randomly chosen respondents are a better guide to what all Americans think than the opinions of 186,000 callers

Local draft boards Prior to 1970, young men were selected for military service by local draft boards. Th ere was a complex system of exemptions and quotas that allowed, for example, farmers sons and married young men with children to avoid the draft . Do you think that random selection among all men of the same age is preferable to making distinctions based on marital status? Give your reasons.

Random selection? Choosing at random is a fair way to decide who gets some rare prize, in the sense that everyone has the same chance to win. Random choice isnt always a good ideasometimes we dont want to treat everyone the same, because some people have a better claim. In each of the following situations, would you support choosing at random? Give your reasons in each case. (a) Th e basketball arena has 4000 student seats, and 7000 students want tickets. Should we choose 4000 of the 7000 at random? (b) Th e list of people waiting for liver transplants is much larger than the number of available livers. Should we let chance decide who gets a transplant?

How much do students earn? A universitys fi nancial aid offi ce wants to know how much it can expect students to earn from summer employment. Th is information will be used in setting the level of fi nancial aid. Th e population contains 3478 students who have completed at least one year of study but have not yet graduated. Th e university will send a questionnaire to an SRS of 100 of these students, drawn from an alphabetized list. (a) Describe how you will label the students in order to select the sample. (b) Use Table B, beginning at line 105, to select the fi rst 5 students in the sample.

More randomization Most sample surveys call residential telephone numbers at random. Th ey do not, however, always ask their questions of the person who picks up the phone. Instead, they ask about the adults who live in the residence and choose one at random to be in the sample. Why is this a good idea?

A biased sample You see a female student standing in front of the cafeteria, now and then stopping other students to ask them questions. She says that she is conducting a survey of student opinions about the quality of food in the cafeteria. Explain why this sampling method is almost certainly biased.

Sampling TVs An electronics company has 50 large fl at-screen televisions ready for shipment, each labeled with one of the following serial numbers: A1109 A2056 A2219 A2381 B0001 A1123 A2083 A2336 A2382 B0012 A1186 A2084 A2337 A2383 B0046 A1197 A2100 A2338 A2384 B1195 A1198 A2108 A2339 A2385 B1196 A2016 A2113 A2340 A2390 B1197 A2017 A2119 A2351 A2396 B1198 A2020 A2124 A2352 A2410 B1199 A2029 A2125 A2367 A2410 B1200 A2032 A2130 A2372 A2500 B1201 An SRS of 5 TVs must be chosen for inspection. Use Table B to do this, beginning at line 139. Explain your method clearly

Gun control Since the beginning of opinion polls over 50 years ago, at least two-thirds of those surveyed said that they favored stronger controls on fi rearms. Specifi c gun control proposals have oft en been favored by 80% to 85% of respondents. Yet little national gun control legislation has passed, and no major national restrictions on fi rearms exist. Why do you think this has occurred?

A lottery for drugs? Only limited supplies of some experimental drugs are available because the drugs are very diffi cult to make. Sometimes it is necessary to use a lottery to decide at random which patients can receive a drug that is in short supply. Several years ago, for example, Hoff manLa Roche had enough doses of the drug Invirase for 2880 AIDS patients. Shortly aft er announcing this, the company received 10,000 calls from patients who wanted to enter the lottery. Discuss this practice. Do you favor random selection? If not, how should recipients be chosen?

Read anything lately? Th e Denver Public Library wants to estimate the percent of Denver households with an adult who has read at least one book in the last month. Th e homes of 400 people who have library cards are sampled, and it turns out that 90% of these households have an adult who has read a book in the past month. Is 90% likely to be a biased estimate for the true percent of Denver households with an adult who has read at least one book in the last month? Explain why or why not

Women count! Broadcast and print media across the country have reported on the governments release of a report on the status of working women called Working Women Count. Th is report gives fi ndings from a survey of 250,000 women. According to one news report: More than 1600 businesses, unions, newspapers, magazines, and community service organizations helped distribute the survey to their members, subscribers, and patrons, which the White House announced with much fanfare. It sought womens opinions on job satisfaction, pay, benefi ts, and opportunities for advancement.6 A second survey, asking the same questions, was conducted at the same time. However, this survey interviewed only 1200 working women chosen at random. Which survey is likely to give a more accurate view of working womens opinions on job satisfaction, pay, benefi ts, and opportunities for advancement? Explain briefl y.

Stop smoking! A random sample of 1000 people who signed a card saying they intended to quit smoking were contacted 9 months later. It turned out that 210 (21%) of the sampled individuals had not smoked over the past 6 months. Specify the population of interest, the parameter of interest, the sample, and the sample statistic in this problem. Each boldface number in Exercises 5.28 to 5.30 is the value of either a parameter or a statistic. In each case, state which it is.

Drink Arizona On Tuesday, the bottles of Arizona iced tea fi lled in a plant were supposed to contain an average of 20 ounces of iced tea. Quality control inspectors sampled 50 bottles at random from the days production. Th ese bottles contained an average of 19.6 ounces of iced tea.

Flight safety On a New YorktoDenver fl ight, 8% of the 125 passengers were selected for random security screening prior to boarding. According to the Transportation Security Administration, 10% of airline passengers are chosen for random screening

Sleeping ducks, I A recent report in the journal Nature examined whether ducks keep an eye out for predators while they sleep. Th e researchers, from Indiana State University, put four ducks in each of four plastic boxes, which were arranged in a row. Ducks in the two end boxes slept with one eye open 31.8% of the time, compared with only 12.4% of the time for the ducks in the two center boxes

Sleeping ducks, II Is the study described in the previous exercise an example of an observational study or a comparative experiment? Explain briefl y.

Dead trees On the west side of Rocky Mountain National Park, many mature pine trees are dying due to infestation by pine beetles. Scientists would like to use sampling to estimate the proportion of all pine trees in the area that have been infected. (a) Explain why it wouldnt be practical for scientists to obtain an SRS in this setting. (b) A possible alternative would be to use every pine tree along the parks main road as a sample. Why is this sampling method biased? (c) Suppose that a more complicated random sampling plan is carried out, and that 35% of the pine trees in the sample are infested by the pine beetle. Can scientists conclude that 35% of all the pine trees on the west side of the park are infested? Why or why not?

Bias and variability Figure 5.8 (on the facing page) shows the behavior of a sample statistic in many samples in four situations. Th ese graphs are like those in Figures 5.5 and 5.6. Th at is, the heights of the bars show how oft en the sample statistic took various values in many samples from the same population. Th e true value of the population parameter is marked by an arrow on each graph. Label each of the graphs in Figure 5.8 as showing high or low bias and as showing high or low variability.

Sampling variability In thinking about Gallups sample of size 1523, we asked, Could it happen that one random sample finds that 57% of adults recently bought a lottery ticket and a second random sample finds that only 37% had done so? Look at Figure 5.6 (page 224), which shows the results of 1000 samples of this size when the population truth is 60%. Would you be surprised if a sample from this population gave 57%? Would you be surprised if a sample gave 37%?

No hands! Students from Hunter College in New York City carried out an observational study of driver behaviors at 50 diff erent intersections. Of the 3120 drivers they observed, 23% were talking on cell phones. (a) In national surveys of driver behavior, well over half of those surveyed admit that they regularly talk on cell phones while driving. Give at least two reasons why the Hunter College study gave such diff erent results. (b) If the Hunter College students had observed twice as many drivers, would the percent of drivers talking on cell phones have been about the same as the results from national surveys? Why or why not?

Predict the election Just before a presidential election, a national opinion poll increases the size of its weekly sample from the usual 1500 people to 4000 people. (a) Does the larger random sample reduce the bias of the poll result? Explain. (b) Does it reduce the variability of the result? Explain.

A sampling simulation Let us illustrate sampling variability in a small sample from a small population. Ten of the 25 club members listed below are female. Th eir names are marked with asterisks in the list. Th e club chooses 5 members at random to receive free trips to the national convention. Alonso Darwin Herrnstein Myrdal Vogt* Binet* Epstein Jimenez* Perez* Went Blumenbach Ferri Luo Spencer* Wilson Chase* Gonzales Moll* Th omson Yerkes Chen* Gupta* Morales* Toulmin Zimmer (a) Draw 20 SRSs of size 5, using a diff erent part of Table B each time. Record the number of females in each of your samples. (b) Make a dotplot to display your results. What is the average number of females in your 20 samples? (c) Do you think the club members should suspect discrimination if none of the 5 tickets goes to a woman? Justify your answer.

Canadas national health care Th e Ministry of Health in the Canadian province of Ontario wants to know whether the national health care system is achieving its goals in the province. Much information about health care comes from patient records, but that source doesnt allow us to compare people who use health services with those who dont. So the Ministry of Health conducted the Ontario Health Survey, which interviewed a random sample of 61,239 people who live in the province of Ontario.9 (a) What is the population for this sample survey? What is the sample? (b) Th e survey found that 76% of males and 86% of females in the sample had visited a general practitioner at least once in the past year. Do you think these estimates are close to the truth about the entire population? Why?

Take a bigger sample A student is planning a project on student attitudes toward part-time work while attending school. She develops a questionnaire and plans to ask 25 randomly selected students to fi ll it out. Her statistics teacher approves the questionnaire but suggests that the sample size be increased to at least 100 students. Why is the larger sample helpful? Back up your answer by using the quick method to estimate the margin of error for samples of size 25 and for samples of size 100.

Find the margin of error Example 5.12 tells us that Gallup asked 501 teenagers whether they approved of legal gambling; 52% said they did. Use the quick method to estimate the margin of error for conclusions about all teenagers. How does your result compare with Gallups margin of error quoted in Example 5.12?

The Current Population Survey Though opinion polls usually make 95% confidence statements, some sample surveys use other confidence levels. The monthly unemployment rate, for example, is based on the Current Population Survey of about 50,000 households. The margin of error in the unemployment rate is announced as about two-tenths of 1 percentage point with 90% confidence. Would the margin of error for 95% confidence be smaller or larger? Why?

Polling women Many years ago, a New York Times Poll on womens issues interviewed 1025 women randomly selected from the United States, excluding Alaska and Hawaii. One question was Many women have better jobs and more opportunities than they did 20 years ago. Do you think women had to give up too much in the process, or not? Forty-eight percent of women in the sample said Yes.10 (a) Th e poll announced a margin of error of 63 percentage points for 95% confi dence in its conclusions. Make a 95% confi dence statement about the percent of all adult women who felt that women had to give up too much. (b) Explain to someone who knows no statistics why we cant just say that 48% of all adult women felt that women had to give up too much. (c) Explain clearly what 95% confi dence means.

Polling men and women Th e sample survey described in Exercise 5.42 interviewed 472 randomly selected men as well as 1025 women. Th e poll announced a margin of error of 63 percentage points for 95% confi dence in conclusions about women. Th e margin of error for results concerning men was 65 percentage points. Why is this larger than the margin of error for women?

Is there a heaven? A news article reports that in a recent opinion poll, 81% of a sample of 1003 adults said they believe there is a heaven. (a) Use the quick method to estimate the margin of error for a sample of this size. (b) Make a confi dence statement about the percent of all adults who believe there is a heaven.

Strike three A survey is conducted in Chicago (population 2,800,000) using random digit dialing equipment that places calls at random to residential phones, both listed and unlisted. Th e purpose of the survey is to determine the percent of Chicagoans who support the three strikes and youre out provision of the crime bill passed by Congress. One-tenth of 1% of the adult population is interviewed, and 53% of them favor the proposal. A second survey is taken in Dayton, Ohio (population 156,000), using the same techniques and asking the same question of one-tenth of 1% of the adults living in Dayton. Which survey is more likely to produce a sample result that is closer to the truth about the population in that city? Explain briefly

Presidential polls California has about four times as many voters as Ohio, but both are very important states for the outcome of any presidential election. One national polling organization plans to take surveys of 1000 randomly selected voters in each of these two states on the day before the election. In which state is the survey more likely to accurately predict the states election results? Explain. Each boldface number in Exercises 5.47 and 5.48 is the value of either a parameter or a statistic. In each case, state which it is.

Left ies According to Real Facts at Snapple.com, 13% of adults are left - handed. At a math teachers conference, 16% of those attending were left -handed.

Single-sex classes In an experiment to test the eff ectiveness of single-sex classrooms, girls assigned at random to a coeducational chemistry class gained an average of 12.2 points from a pretest to a posttest. Girls assigned randomly to a single-sex chemistry class taught by the same teacher gained 15.1 points.

Find the margin of error Exercise 5.38 (page 228) describes a sample survey of 61,239 adults living in Ontario. About what is the margin of error for conclusions having 95% confi dence about the entire adult population of Ontario? Show your work.

Explaining confi dence A student reads that we are 95% confi dent that the average score of young men on the quantitative part of the National Assessment of Educational Progress is 267.8 to 276.2. Asked to explain the meaning of this statement, the student says, 95% of all young men have scores between 267.8 and 276.2. Is the student right? Explain your answer

Teens on the Net A poll of 1070 teens aged 13 to 17 fi nds that 742 have received personal messages online from people they dont know. Th e announced margin of error for this result is plus or minus 3 percentage points. Th e news report does not give the confi dence level, but you can be quite sure that its 95%. (a) What is the value of the sample proportion p^ who have received personal messages online from people they dont know? Explain in words what the population parameter p is in this setting. (b) Make a confi dence statement about the parameter p

Protecting teens Th e previous exercise describes a sample survey of 1070 teens, with margin of error 63% for 95% confi dence. (a) An agency that is responsible for protecting children thinks that 95% confi - dence is not enough. Th ey want to be 99% confi dent. How would the margin of error for 99% confi dence based on the same sample compare with the margin of error for 95% confi dence? (b) A parents group is satisfi ed with 95% confi dence but wants a smaller margin of error than 63%. How can we get a smaller margin of error, still with 95% confi dence?

Video gaming In a 2006 poll, 40% of American adults surveyed said that they play computer or video games. Of those who played such games, 10% reported playing for 10 or more hours per week. According to the Associated Press, Th e results are taken from a poll of 3,024 adults, including 1,046 who play electronic games, that was conducted April 1827. Th e poll, conducted by the international polling fi rm Ipsos, has a margin of sampling error of plus or minus 2 percentage points, 3 points for the sample of those who play electronic games.11 (a) Use the quick method to show that the margins of error quoted above are approximately correct if a simple random sample was taken. (b) Th e confi dence level wasnt stated, but its almost certainly 95%. Make an appropriate confi dence statement about video gaming in the population of American adults. (c) Identify two possible sources of error in this survey that the margin of error does not include. (d) If this survey were repeated today, do you think the results would be about the same? Do some research to fi nd whether your suspicion is correct

Simulating summer employment Random digits can be used to simulate the results of random sampling. Suppose that you are drawing simple random samples of size 25 from a large number of college students and that 20% of the students are unemployed during the summer. To simulate this SRS, let 25 consecutive digits in Table B stand for the 25 students in your sample. Th e digits 0 and 1 stand for unemployed students, and other digits stand for employed students. Th is is an accurate imitation of the SRS because 0 and 1 make up 20% of the 10 equally likely digits. Simulate the results of 50 samples by counting the number of 0s and 1s in the fi rst 25 entries in each of the 50 rows of Table B. Make a histogram like the one in Figure 5.5 to display the results of your 50 samples. Is the truth about the population (20% unemployed, or 5 in a sample of 25) near the center of your graph? What are the smallest and largest counts of unemployed students you obtained in your 50 samples? What percent of your samples had either 4, 5, or 6 unemployed?

Not in the margin of error A recent Gallup Poll found that 68% of adult Americans favor teaching creationism along with evolution in public schools. Th e Gallup press release says: For results based on samples of this size, one can say with 95 percent confi dence that the maximum error attributable to sampling and other random eff ects is plus or minus 3 percentage points.16 Give one example of a source of error in the poll result that is not included in this margin of error.

What kind of error? Which of the following are sources of sampling error and which are sources of nonsampling error? Explain your answers. (a) Th e subject lies about past drug use. (b) A typing error is made in recording the data. (c) Data are gathered by asking people to mail in a coupon printed in a newspaper.

Internet users then A survey of Internet users in 1995 found that males outnumbered females by nearly 2 to 1. Th is was a surprise, because earlier surveys had put the ratio of men to women closer to 9 to 1. Later in the article we fi nd this information: Detailed surveys were sent to more than 13,000 organizations on the Internet; 1,468 usable responses were received. According to Mr. Quarterman, the margin of error is 2.8 percent, with a confi dence level of 95 percent.17 (a) What was the response rate for this survey? (Th e response rate is the percent of the planned sample that responded.) (b) Use the quick method (page 229) to estimate the margin of error of this survey. Is your result close to the 2.8% claimed? (c) Is the small margin of error a good measure of the accuracy of the surveys results? Explain your answer.

Polling students A high school chooses an SRS of 100 students from the schools attendance list to interview about student life. If it selected two SRSs of 100 students at the same time, the two samples would give somewhat diff erent results. Is this variation a source of sampling error or of nonsampling error? Will the surveys announced margin of error take this source of error into account?

Internet users now Who uses the Internet more todaymales or females? Find a report of a recent survey that you believe provides accurate information on this question. Print the article if possible. Be sure to record all source information. Write a brief report following the four-step statistical problem-solving process (page 19).

Activity 5.3 follow-up Return to the survey your team constructed in Activity 5.3 (page 236). Discuss how your design protects against (a) sampling errors. (b) nonsampling errors.

A sampling paradox? Example 5.19 compares two SRSsof a universitys undergraduate and graduate students. Th e sample of undergraduates contains a smaller fraction of the population, 1 out of 90, versus 1 out of 15 for graduate students. Yet sampling 1 out of 90 undergraduates gives a smaller margin of error than sampling 1 out of 15 graduate students. Explain to someone who knows no statistics why this happens.

Scholar-athletes To ask about their future plans, you want to interview 10 students at your high school who have received athletic scholarships to attend college. Because you believe there may be large diff erences among athletes in diff erent sports, you decide to interview a stratifi ed random sample of 7 basketball players and 3 golfers. Use Table B, beginning at line 101, to select your sample from the team rosters below. Explain your method carefully enough that a classmate could obtain your results. BASKETBALL Arenas Duncan Leslie Robinson Billups Farmar McGrady Stoudamire Brand Fowles Miller Taurasi Bryant Gasol Nowitzki Wade Carter Iverson Parker GOLF Creamer Kim Singh Els Mickelson Wie Gulbis Prammanasudh Woods

Genetically modifi ed foods An article in the journal Science looks at diff erences in attitudes toward genetically modifi ed foods in Europe and the United States. Th is calls for sample surveys. Th e European survey chose a sample of 1000 adults in each of 17 European countries. Heres part of the description: Th e Eurobarometer survey is a multistage, random-probability face-to-face sample survey.20 (a) What does multistage mean? (b) You can see that the fi rst stage was stratifi ed. What were the strata? (c) What does random-probability sample mean?

Wording of questions A New York Times/CBS News Poll asked a random sample of Americans about abortion: Do you think there should be an amendment to the Constitution prohibiting abortions, or shouldnt there be such an amendment? Th e same people were later asked, Do you believe there should be an amendment to the Constitution protecting the life of the unborn child, or shouldnt there be such an amendment? For one of the questions, 50% were in favor and 39% were opposed. For the other, 29% were in favor and 62% were opposed. (Th e rest were uncertain.)21 Which question do you think yielded each result? Explain why.

Closed versus open questions Two basic types of questions are closed questions and open questions. A closed question asks the subject for one or more of a fi xed set of responses. An open question allows the subject to answer in his or her own words. Th e interviewer writes down the responses and sorts them later. An example of an open question is How do you feel about broccoli? An example of a closed question is What is your opinion about broccoli? Do you a. like it very much? b. like it somewhat? c. neither like nor dislike it? d. dislike it somewhat? e. dislike it very much? What are the advantages and disadvantages of open and closed questions?

Bad survey questions Write your own examples of bad sample survey questions. (a) Write a biased question designed to get one answer rather than another. (b) Write a question that is confusing, so that it is hard to answer.

Systematic random sample Th e fi nal stage in a multistage sample must choose 5 of the 500 addresses in a neighborhood. You have a list of the 500 addresses in geographical order. To choose a systematic random sample, proceed as follows: Step 1. Choose 1 of the fi rst 100 addresses on the list at random. (Label them 00, 01, . . . , 99 and use a pair of digits from Table B to make the choice.) Step 2. Th e sample consists of the address from Step 1 and the addresses 100, 200, 300, and 400 positions down the list from it. If 71 is chosen at random in Step 1, for example, the systematic random sample consists of the addresses numbered 71, 171, 271, 371, and 471. (a) Use Table B to choose a systematic random sample of 5 from a list of 500 addresses. Enter the table at line 130. (b) What is the chance that any specifi c address will be chosen? Explain your answer. (c) Explain why this sample is not an SRS.

A stratifi ed sample A university has 2000 male and 500 female faculty members. Th e university president wants to poll the opinions of a random sample of faculty members. In order to give adequate attention to female faculty opinion, the president decides to choose a stratifi ed random sample of 200 males and 200 females. Th e president obtains alphabetized lists of female and male faculty members. (a) Explain how you would assign labels and use random digits to choose the desired sample. Enter Table B at line 122 and give the fi rst 5 females and the fi rst 5 males in your sample. (b) What is the chance that any one of the 2000 males will be in your sample? What is the chance that any one of the 500 females will be in your sample? (c) Each member of the sample is asked, In your opinion, are female faculty members in general paid less than males with similar positions and qualifi cations? 180 of the 200 females (90%) say Yes. 60 of the 200 males (30%) say Yes. In all, 240 of the sample of 400 (60%) answered Yes. Th e president therefore reports: Based on a sample, we can conclude that 60% of the total faculty feel that female members are underpaid relative to males. Explain why this conclusion is wrong. (d) If we took a stratifi ed random sample of 200 male and 50 female faculty members at this university, each member of the faculty would have the same chance of being chosen. What is that chance? Explain why this sample is not an SRS.

Women engineers About 20% of the engineering students at a large university are women. Th e school plans to poll a sample of 200 engineering students about the quality of student life. (a) If an SRS of size 200 is selected, about how many women do you expect to fi nd in the sample? (b) If the poll wants to be able to report separately the opinions of male and female students, what type of sampling design would you suggest? Why?

Video gaming In a 2006 poll, 40% of American adults surveyed said that they play computer or video games. Of those who played such games, 10% reported playing for 10 or more hours per week. According to the Associated Press, Th e results are taken from a poll of 3,024 adults, including 1,046 who play electronic games, that was conducted April 1827. Th e poll, conducted by the international polling fi rm Ipsos, has a margin of sampling error of plus or minus 2 percentage points, 3 points for the sample of those who play electronic games.11 (a) Use the quick method to show that the margins of error quoted above are approximately correct if a simple random sample was taken. (b) Th e confi dence level wasnt stated, but its almost certainly 95%. Make an appropriate confi dence statement about video gaming in the population of American adults. (c) Identify two possible sources of error in this survey that the margin of error does not include. (d) If this survey were repeated today, do you think the results would be about the same? Do some research to fi nd whether your suspicion is correct

Multistage sampling Th e previous exercise gives part of the description of a sample survey from the Wall Street Journal. (a) It appears that the sample was taken in several stages. Why can we say this? (b) Th e fi rst stage no doubt used a stratifi ed sample, though the Journal does not say this. Explain why it would be bad practice to use an SRS from a large number of geographic points across the country rather than a stratifi ed sample of such points.

TV ratings Th e method of collecting the data can infl uence the accuracy of sample results. Th e following methods have been used to collect data on television viewing in a sample household: (a) Diary method. Th e household keeps a diary of all programs watched and who watched them for a week, then mails in the diary at the end of the week. (b) Roster-recall method. An interviewer shows the person a list of programs for the preceding week and asks which programs were watched. (c) Telephone-coincidental method. Th e survey fi rm telephones the household at a specifi c time and asks if the television is on, which program is being watched, and who is watching it. (d) Automatic recorder method. A device attached to the set records what hours the set is on and to which channel it is tuned. At the end of the week, this record is removed from the recorder. (e) People meter. Each member of the household is assigned a numbered button on a hand-held remote control. Everyone is asked to push their button whenever they start or stop watching TV. Th e remote control signals a device attached to the set that keeps track of what channel the set is tuned to and who is watching at all times. Discuss the advantages and disadvantages of each of these methods, especially the possible sources of error associated with each method. Th e Nielsen national ratings use Method (e). Local ratings (there are more than 200 local television markets) use Method (a). Do you agree with these choices? (Do not discuss choosing the sample, just collecting the data once the sample is chosen.)

Did you vote? When the Current Population Survey asked the adults in its sample of 50,000 households if they voted in the most recent presidential election, 54% said they had. In fact, only 49% of the adult population voted in that election. (a) Use the quick method to estimate the margin of error for this survey. (Although the CPS sample is not an SRS, the quick method still gives a reasonably accurate estimate of the margin of error.) (b) Why do you think the CPS result missed by much more than the margin of error?

Telling the truth? Many people dont give honest answers to questions about illegal or sensitive issues. One study divided a large group of adults into thirds at random. All were asked if they had ever used cocaine. Th e fi rst group was interviewed by telephone: 21% said Yes. In the group visited at home by an interviewer, 25% said Yes. Th e fi nal group was interviewed at home but answered the question on an anonymous form that they sealed in an envelope. Of this group, 28% said they had used cocaine.23 (a) Which result do you think is closest to the truth? Why? (b) Give two other examples of behavior you think would be underreported in a telephone survey.

What kind of error? Each of the following is a source of error in a sample survey. Label each as sampling error or nonsampling error, and explain your answers. (a) Th e telephone directory is used as a sampling frame. (b) Th e person cannot be contacted in fi ve calls. (c) Interviewers choose people walking by on the sidewalk to interview.

Survey time! Return to Activity 5.3 (page 236). Once your teacher has approved your survey design plan, go ahead and carry it out. Write a brief report summarizing the results. Follow the four-step statistical problem-solving process (page 19).

Baseball tickets Suppose you want to know the average amount of money spent by the fans attending opening day for the Cleveland Indians baseball season. You get permission from the teams management to conduct a survey at the stadium, but they will not allow you to bother the fans in the club seating or box seat areas (the most expensive seating). Using a computer, you randomly select 500 seats from the rest of the stadium. During the game, you ask the fans in those seats how much they spent that day. (a) Provide a reason why this survey might yield a biased result. (b) Explain whether the reason you provided in (a) is a sampling error or a nonsampling error.

Dress code? Th e principal has asked your statistics class to carry out a survey of student opinion about a proposed dress code. Th e class decides to choose four of its members at random to meet with the principal. Th e class list appears below. Choose an SRS of 4 using Table B, beginning at line 145. Explain your method clearly enough for a classmate to duplicate your results. Anderson Fernandez Kempthorn Robertson Aspin Gupta Liang Rodriguez Benitez Gutierrez Montoya Siegel Bock Gwynn Olds Tompkins Breiman Harter Patnaik Vandegraff Castillo Henderson Pirelli Wang Dixon Hughes Rao Edwards Johnson Rider

We dont like one-way streets Highway planners decided to make a main street in West Lafayette, Indiana, a one-way street. Th e Lafayette Journal and Courier took a one-day poll by inviting readers to call a telephone number to record their comments. Th e next day, the paper reported: Journal and Courier readers overwhelmingly prefer two-way traffi c fl ow in West Lafayettes Village area to one-way streets. By nearly a 7-1 margin, callers to the newspapers Express Yourself opinion line on Wednesday complained about the oneway streets that have been in place since May. Of the 98 comments received, all but 14 said no to one-way. (a) What population do you think the newspaper wants information about? (b) Is the proportion of this population who favor one-way streets almost certainly larger or smaller than the proportion 14/98 in the sample? Why?

TV commercials Th e noted scientist Dr. Iconu wanted to investigate attitudes toward television advertising among American college students. He decided to use a sample of 100 students. Students in freshman psychology (PSY 001) are required to serve as subjects for experimental work. Dr. Iconu obtained a class list for PSY 001 and chose a simple random sample of 100 of the 340 students on the list. He asked each of the 100 students in the sample the following question: Do you agree or disagree that having commercials on TV is a fair price to pay for being able to watch it? Of the 100 students in the sample, 82 marked Agree. Dr. Iconu announced the result of his investigation by saying, 82% of American college students are in favor of TV commercials. (a) What is the population in this example? (b) What is the sampling frame in this example? (c) Explain briefl y why the sampling frame is or is not suitable for the question being investigated. (d) Discuss briefl y the question Dr. Iconu asked. Is it a slanted question? (e) Discuss briefl y why Dr. Iconus announced result is misleading. (f) Dr. Iconu defended himself against criticism by pointing out that he had carefully selected a simple random sample from his sampling frame. Is this defense relevant? Why?

Planning a survey of students Th e student government plans to ask a random sample of students at a large high school about their priorities for improving the school newspaper. A school counselor provides a list of the 3500 students at the school to serve as a sampling frame. (a) How would you choose an SRS of 250 students? (b) How would you choose a systematic sample of 250 students? (See Exercise 5.67 page 247, to learn about systematic samples.) (c) Th e list shows whether students are bussed to school (2400 students) or live nearby (1100 students). How would you choose a stratifi ed sample of 200 bussed students and 50 local students? (d) Which of the three sampling methods would you choose? Why?

Bigger samples, please Explain in your own words the advantages of bigger random samples in a sample survey

Should he go or stay? In December 1998, the House of Representatives impeached President Clinton, the fi rst step in removing him from offi ce. Th e Senate then conducted a trial and found the president not guilty. Here are two opinion poll questions asked aft er the House had acted: What do you think President Clinton should do: fi ght the charges in the Senate, or resign from offi ce? What do you think President Clinton should do: continue to serve and stand trial in the Senate, or resign from offi ce? In response to the fi rst question, 58% thought the president should resign. But only 43% of those asked the second question thought he should resign.24 Why do you think the fi rst wording encouraged more people to favor resignation?

The Harris Poll Here is the language used by the Harris Poll to explain the accuracy of its results: In theory, with a sample of this size, one can say with 95 percent certainty that the results have a statistical precision of plus or minus 3 percentage points of what they would be if the entire adult population had been polled with complete accuracy.25 What does Harris mean by 95 percent certainty?

Steroids in baseball A 2008 New York Times article on public opinion about steroid use in baseball discussed the results of a sample survey. Th e survey found that 34% of adults think that at least half of Major League Baseball (MLB) players use steroids to enhance their athletic performance. Another 36% thought that about a quarter of MLB players use steroids; 8% had no opinion. Here is part of the Timess statement on How the Poll Was Conducted: Th e latest New York Times/CBS News Poll is based on telephone interviews conducted March 15 through March 18 with 1,067 adults throughout the United States. . . . Th e sample of telephone numbers called was randomly selected by a computer from a list of more than 42,000 active residential exchanges across the country. Th e exchanges were chosen to ensure that each region of the country was represented in proportion to its population. In each exchange, random digits were added to form a complete telephone number, thus permitting access to listed and unlisted numbers. In each household, one adult was designated by a random procedure to be the respondent for the survey.

Life and Internet A poll of 586 adults who used the Internet in the past week were asked whether the Internet has made your life much better, somewhat better, somewhat worse, much worse, or has it not aff ected your life either way. In all, 152 of the 586 said much better.26 (a) What is the population for this sample survey? (b) Use the quick method to fi nd a margin of error. Th en give a complete confi dence statement for a conclusion about the population.