Chapter 8 EPSDue 11/13/15

• A sample survey selects a _____________ from the _________________ of all

individuals about which we desire information. We base __________________ about

the population on data from the sample. It is important to specify exactly what

_________________ you are interested in and what ______________ you will measure.

• The ____________ of a sample describes the method used to select the sample

from the population. ________________ sampling designs use chance to select a

sample.

• The basic random sampling design is a _________ ___________ ____________(SRS).

An SRS gives every possible sample of a given size the same ____________ to be chosen.

• Choose an SRS by labeling the members of the population and using ___________ digits to

select the sample. Software can automate this process.

• To choose a ______________ random sample, classify the population into __________,

groups of individuals that are ________________ in some way that is important to the

response. Then choose a separate _______ from each stratum.

• Failure to use _____________ sampling often results in ___________, or systematic

errors in the way the ____________ represents the ___________________.

_________________ ________________ samples, in which the respondents choose

themselves, are particularly prone to large bias.

• In human populations, even random samples can suffer from __________ due to

_________________ or _____________, from _______________ bias, or from

misleading results due to _____________ _____________questions. Sample surveys

must deal expertly with these potential problems in addition to using a random sampling

design.

• Most national sample surveys are carried out by ____________, using random digit dialing

to choose residential telephone numbers at random. Because ________ __________ is

increasing nonresponse to such surveys, and the rise of ______-_______-__________

households is increasing ___________________, many surveys include a minimum quota of

cell phone users in their samples to help adjust for bias.

Web surveys are becoming more frequent, but many suffer from _______________ response,

__________________, and ___________________.

• A sample survey selects a sample from the population of all individuals about which we desire information. We base conclusions about the population on data from the sample. It is important to specify exactly what population you are interested in and what variables you will measure.

• The design of a sample describes the method used to select the sample from the population. Random sampling designs use chance to select a sample.

• The basic random sampling design is a simple random sample (SRS). An SRS gives every possible sample of a given size the same chance to be chosen.

• Choose an SRS by labeling the members of the population and using random digits to select the sample. Software can automate this process.

• To choose a stratified random sample, classify the population into strata, groups of individuals that are similar in some way that is important to the response. Then choose a separate SRS from each stratum.

• Failure to use random sampling often results in bias, or systematic errors in the way the sample represents the population. Voluntary response samples, in which the respondents choose themselves, are particularly prone to large bias.

• In human populations, even random samples can suffer from bias due to undercoverage or nonresponse, from response bias, or from misleading results due to poorly worded questions. Sample surveys must deal expertly with these potential problems in addition to using a random sampling design.

• Most national sample surveys are carried out by telephone, using random digit dialing to choose residential telephone numbers at random. Because call screening is increasing nonresponse to such surveys, and the rise of cell-phone-only households is increasing undercoverage, many surveys include a minimum quota of cell phone users in their samples to help adjust for bias. Web surveys are becoming more frequent, but many suffer from volunteer response, undercoverage, and nonresponse.

8.17 An online store contacts 1000 customers from its list of customers who have purchased in the last year. In all, 696 of the 1000 say that they are very satisfied with the store’s website. The population in this setting is

(a)all customers who have purchased something in the last year.

(b)the 1000 customers contacted.

(c)the 696 customers who were very satisfied with the store’s website.

8.18 A state representative wants to know how voters in his district feel about enacting a statewide smoking ban in all enclosed public places, including bars and restaurants, as well as several other current statewide issues. He mails a questionnaire addressing these issues to an SRS of 800 voters in his district. Of the 800 questionnaires mailed, 152 were returned. The sample is

(a)the 800 voters receiving the questionnaire.

(b)the 152 voters returning the questionnaire.

(c)all voters in his district.

8.19 In the survey for Exercise 8.18, there are 8741 registered voters in his district. You label the voters 0001 to 8741 in alphabetical order. Using line 123 of Table B to select the sample, the first five voters in your sample would be

(a)5458, 0815, 7271, 2560, 2755.

(b)5458, 0815, 0727, 1025, 6027.

(c)5458, 8150, 7271, 2560, 2755.

8.20 The website www.twiigs.com allows you to vote on polls that interest you or to post one of your own. Once you have found a poll of interest, you just click on “Vote,” and your response becomes part of the sample. One of the questions in July 2010 was, “How many times have you been pulled over by the police?” Of the 780 people responding, 70% said “1-5 times.” You can conclude that

(a)about 70% of Americans have been pulled over by the police “1-5 times.”

(b)the poll uses voluntary response, so the results tell us little about the population of all adults.

(c)more people still need to vote on the question, as a larger sample is required to reduce bias.

8.21 Archaeologists plan to examine a sample of two-meter-square plots near an ancient Greek city for artifacts visible in the ground. They choose separate samples of plots from floodplain, coast, foothills, and high hills. What kind of sample is this?

(a)A simple random sample

(b)A stratified random sample

(c)A voluntary response sample

8.22 You must choose an SRS of 10 of the 440 retail outlets in New York that sell your company’s products. How would you label this population to select a simple random sample?

(a)001, 002, 003,…, 439, 440

(b)000, 001, 002,…, 439, 440

(c)1, 2,…, 439, 440

8.23 You are using the table of random digits to choose a simple random sample of six students from a class of 30 students. You label the students 01 to 30 in alphabetical order, and then select a simple random sample. Which of the following is a possible sample that could be obtained?

(a)45, 74, 04, 18, 07, 65

(b)04, 18, 07, 13, 02, 07

(c)04, 18, 07, 13, 02, 05

8.24 A sample of households in a community is selected at random from the telephone directory. In this community, 4% of households have no telephone, 10% have only cell phones, and another 25% have unlisted telephone numbers. The sample will certainly suffer from

(a)nonresponse.

(b)undercoverage.

(c)false responses.

8.25 The Pew Research Centers Report entitled “How Americans value public libraries in their communities,” released December 11, 2013, asked a random sample of 6224 Americans aged 16 and over, “Have you used a Public Library website in the last 12 months?” In the entire sample, 30% said “yes.” But only 17% of those in the sample over 65 years of age said “yes.” Which of these two sample percents will be more accurate as an estimate of the truth about the population?

(a)The result for those over 65 is more accurate because it is easier to estimate a proportion for a small group of people.

(b)The result for the entire sample is more accurate because it comes from a larger sample.

(c)Both are equally accurate because both come from the same sample.

8.28 Stormwater pollution. The administrators of the city’s Stormwater Program are interested in evaluating the public’s knowledge of the causes and effects of stormwater pollution. They set up an information booth at the city’s Earth Day celebration, and people who visit the booth are offered the opportunity to complete a survey on their knowledge of stormwater pollution.

(a)If the population of interest is adult residents of the city, discuss any sources of bias that might limit the usefulness in using this survey to draw conclusions about this population.

(b)The survey at the Earth Day celebration was intended to be used as a pilot study to make sure the questions were not ambiguous. The full survey is to be an online survey. Residents are to be made aware of the survey through information mailed with their utility bills, and asked to go online to complete the survey. Discuss any sources of bias that might be contained in the full survey.

(c)Suppose we select a random sample of utility customers. Only the residents in the sample are to be made aware of the survey through information mailed with their utility bills, and asked to go online to complete the survey. Does this have any advantages or disadvantages over the full survey in part (b) in terms of possible bias? Explain.

8.29 Sampling telephone area codes. The United States currently has approximately 287 Numbering Plan Areas (NPAs) in service, corresponding to geographic regions. Each NPA is identified by a three-digit code, commonly called an area code. (More are created regularly.)20 You want to choose an SRS of 20 of these area codes for a study of available telephone numbers. Label the codes 001 to 287, and use the Simple Random Sample applet or other software to choose your sample. (If you use Table B, start at line 122 and choose only the first five area codes in the sample.)

8.30 Paying taxes. In April 2014, a Gallup Poll asked two questions about the amount one pays in federal income taxes.21 Here are the two questions:

Question A: Do you regard the income tax which you will have to pay this year as fair?

Question B: Do you consider the amount of federal income tax you have to pay as too high, about right, or too low?

One of these questions drew 52% saying the amount was fair or about right; the other, only 41%. Which wording produced the higher percentage? Why?

8.31 Wording of questions. Do the opinions of Canadians and Americans differ on the right of citizens to bear arms? Although the population of the U.S. is about 10 times that of Canada, the estimated number of privately owned firearms is 25 times higher in the U.S. When Gallup asked a random sample of 1002 American adults the question, “Do you think there should or should not be a law that would ban the possession of handguns, except by the police and other authorized persons?”, 35% said there should be a law banning possession of handguns. At the same time, when Gallup asked a random sample of 1011 Canadians the question, “Do you think the general public should be allowed by law to own a gun?”, 63% said “no.”22 What problems do you see in using the percentages in these two surveys to make a comparison on the opinion on the right to bear arms in the two countries? Explain.

8.35 Running red lights. The sample described in Exercise 8.34 produced a list of 5024 licensed drivers. The investigators then chose an SRS of 880 of these drivers to answer questions about their driving habits.

(a)How would you assign labels to the 5024 drivers? Choose the first five drivers in the sample. If you use Table B, start at line 114.

(b)One question asked was, “Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?” Of the 880 respondents, 171 admitted that at least one light had been red. A practical problem with this survey is that people may not give truthful answers. What is the likely direction of the bias: do you think more or fewer than 171 of the 880 respondents really ran a red light? Why?

8.37 Sampling at a party. At a large block party, there are 40 men and 30 women. You want to ask opinions about how to improve the next party. You choose at random four of the men and separately choose at random three of the women to interview.

(a)What is the probability that any of the 40 men is in your random sample of four men to be interviewed? What is the probability that any of the 30 women is in your random sample of three women to be interviewed?

(b)If you have done the calculations correctly in part (a), the probability of any person at the party being interviewed is the same. Why is your sample of seven men and women not an SRS of people from the party?

8.40 Sampling pharmacists. All pharmacists in the Canadian province of Ontario are required to be members of the Ontario College of Pharmacists. In 2013, there were 13,317 members of the college divided geographically into six voting districts. The number of members in each district follow:

Suppose the college is interested in obtaining members’ views and understanding of the 2012 Expanded Scope of Practice Regulations, which authorizes pharmacists to provide additional services including prescribing drug products for smoking cessation and administering the publicly funded influenza vaccine. To be sure that the opinions of all districts are represented, you choose a stratified random sample of five pharmacists from each district.

Explain how you will assign labels within each district, and then give the label numbers for the five pharmacists in each of Districts H and K who will be part of your sample.

Use software or Table B. If you use Table B, start at line 131 for District H and at line 124 for District K. Why should you not start at the same line in Table B to obtain your samples for Districts H and K?

8.47 Wording survey questions. Comment on each of the following as a potential sample survey question. Is the question sufficiently clear? Is it slanted toward a desired response?

(a)“In light of skyrocketing gasoline prices, we should consider opening up a very small amount of Alaskan wilderness for oil exploration as a way of reducing our dependence on foreign oil. Do you agree or disagree?”

(b)“Do you agree that a national system of health insurance should be favored because it would provide health insurance for everyone and would reduce administrative costs?”

(c)“In view of the negative externalities in parent labor force participation and pediatric evidence associating increased group size with morbidity of children in day care, do you support government subsidies for day care programs?”

8.48 Your own bad 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 to which many people may not give truthful answers.

8.49 The Canadian census. The Canadian government’s decision to eliminate the mandatory long-form version of the census and to move these questions to an optional survey has many concerned. Many members of the business community and economists stressed the importance of the census data for crafting public policy. The minister of industry was given the task of defending the government’s decision. In response to an argument that making the long form of the census voluntary would skew the data by eliminating the statistical randomness of the survey, the minister replied: “Wrong. Statisticians can ensure validity with a larger sample size.”32 Is the minister correct? If not, explain in simple terms the error in his statement.