For Exercises 3.44 and 3.45, see pages 189–190; for Exercise 3.46, see page 192; and for Exercises 3.47, 3.48, and 3.49, see page 193.
3.50 How many text messages? You would like to know something about how many text messages you will receive in the next 100 days. Counting the number for each of the 100 days would take more time than you would like to spend on this project, so you randomly select 10 days from the hundred to count.
(a) Describe the population for this setting.
(b) What is the sample?
3.51 Response rate? A survey designed to assess satisfaction with food items sold at a college’s football games was sent to 150 fans who had season tickets. The total number of fans who have season tickets is 5674. Responses to the survey were received from 98 fans.
(a) Describe the population for this survey.
(b) What is the sample?
(c) What is the response rate?
(d) What is the nonresponse rate?
(e) Suggest some ways that could be used in a future survey to increase the response rate.
3.52 Interview some students. You are a teaching assistant for an introductory statistics class. The instructor would like you to interview some of the students in the class to find out their opinion regarding some new interactive activities that she has introduced to the course. There are 123 students in the class, so you cannot interview all of them. You decide to select eight students to interview.
(a) What is the population for this setting?
(b) What is the sample?
(c) Make a spreadsheet with the numeric labels for the 123 students in the class.
(d) Use Excel to select the labels of the eight students to be interviewed from the spreadsheet.
(e) Explain the steps that you used in sufficient detail so that another person could repeat your work.
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3.53 Interview some students. Refer to the previous exercise.
(a) Use Table B to select the students. Give details.
(b) Compare the use of Table B with software for selecting the students. Which do you prefer? Give reasons for your answer.
3.54 What kind of sample? In each of the following situations, identify the sample as an SRS, a stratified random sample, a multistage random sample, or a voluntary response sample. Explain your answers.
(a) There are seven sections of an introductory statistics course. A random sample of three sections is chosen, and then random samples of eight students from each of these sections are chosen.
(b) A student organization has 55 members. A table of random numbers is used to select a sample of five.
(c) An online poll asks people who visit this site to choose their favorite television show.
(d) Separate random samples of male and female first-year college students in an introductory psychology course are selected to receive a one-week alternative instructional method.
3.55 What’s wrong? Explain what is wrong in each of the following scenarios.
(a) The population consists of all individuals selected in a simple random sample.
(b) In a poll of an SRS of residents in a local community, respondents are asked to indicate the level of their concern about the dangers of dihydrogen monoxide, a substance that is a major component of acid rain and that, in its gaseous state, can cause severe burns. (Hint: Ask a friend who is majoring in chemistry about this substance or search the Internet for information about it.)
(c) Students in a class are asked to raise their hands if they have cheated on an exam one or more times within the past year.
3.56 What’s wrong? Explain what is wrong with each of the following random selection procedures, and explain how you would do the randomization correctly.
(a) To determine the reading level of an introductory statistics text, you evaluate all the written material in the third chapter.
(b) You want to sample student opinions about a proposed change in procedures for changing majors. You hand out questionnaires to 100 students as they arrive for class at 7:30 A.M.
(c) A population of subjects is put in alphabetical order, and a simple random sample of size 10 is taken by selecting the first 10 subjects in the list.
3.57 Importance of students as customers. A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From telephone book listings, the committee chooses 80 businesses at random. Of these, 46 return the questionnaire mailed by the committee.
(a)What is the population for this sample survey?
(b)What is the sample?
(c)What is the rate (percent) of nonresponse?
3.58 Identify the populations. For each of the following sampling situations, identify the population as exactly as possible. That is, say what kind of individuals the population consists of and say exactly which individuals fall in the population. If the information given is not complete, complete the description of the population in a reasonable way.
(a) A college has changed its core curriculum and wants to obtain detailed feedback information from the students during each of the first 12 weeks of the coming semester. Each week, a random sample of five students will be selected to be interviewed.
(b) The American Community Survey (ACS) replaced the census “long form” starting with the 2010 census. The ACS contacts 250,000 addresses by mail each month, with follow-up by phone and in person if there is no response. Each household answers questions about their housing, economic, and social status.
(c) An opinion poll contacts 1161 adults and asks them, “Which political party do you think has better ideas for leading the country in the twenty-first century?”
3.59 Interview residents of apartment complexes. You are planning a report on apartment living in a college town. You decide to select eight apartment complexes at random for in-depth interviews with residents. Select a simple random sample of eight of the following apartment complexes. If you use Table B, start at line 136.
RESIDEN
Ashley Oaks | Country View | Mayfair Village |
Bay Pointe | Country Villa | Nobb Hill |
Beau Jardin | Crestview | Pemberly Courts |
Bluffs | Del-Lynn | Peppermill |
Brandon Place | Fairington | Pheasant Run |
Briarwood | Fairway Knolls | Richfield |
Brownstone | Fowler | Sagamore Ridge |
Burberry | Franklin Park | Salem Courthouse |
Cambridge | Georgetown | Village Manor |
Chauncey Village | Greenacres | Waterford Court |
Country Squire | Lahr House | Williamsburg |
3.60 Using GIS to identify mint field conditions. A Geographic Information System (GIS) is to be used to distinguish different conditions in mint fields. Ground observations will be used to classify regions of each field as either healthy mint, diseased mint, or weed-infested mint. The GIS divides mint-growing areas into regions called pixels. An experimental area contains 100 pixels. For a random sample of 15 pixels, ground measurements will be made to determine the status of the mint, and these observations will be compared with information obtained by the GIS. Select the random sample. If you use Table B, start at line 132 and choose only the first 15 pixels in the sample.
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3.61 Use the Simple Random Sample applet. After you have labeled the individuals in a population, the Simple Random Sample applet automates the task of choosing an SRS. Use the applet to choose the sample in the previous exercise.
3.62 Select a simple random sample. There are 38 active telephone area codes in California. You want to choose an SRS of 10 of these area codes for a study of available telephone numbers. Label the codes 01 to 38 and use the Simple Random Sample applet, Table B, or software to choose your sample. (If you use Table B, start at line 131.)
3.63 Stratified samples for attitudes about alcohol. At a party, there are 25 students over age 21 and 15 students under age 21. You choose at random five of those over 21 and separately choose at random three of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed: what is that chance? Why is your sample not an SRS?
3.64 Systematic random samples. Systematic random samples are often used to choose a sample of apartments in a large building or dwelling units in a block at the last stage of a multistage sample. An example will illustrate the idea of a systematic sample. Suppose that we must choose five addresses out of 125. Because 125/5 = 25, we can think of the list as five lists of 25 addresses. Choose one of the first 25 at random, using software or Table B. The sample contains this address and the addresses 25, 50, 75, and 100 places down the list from it. If 13 is chosen, for example, then the systematic random sample consists of the addresses numbered 13, 38, 63, 88, and 113.
(a) A study of dating among college students wanted a sample of 200 of the 8000 single male students on campus. The sample consisted of every 40th name from a list of the 8000 students. Explain why the survey chooses every 40th name.
(b) Use software or Table B at line 112 to choose the starting point for this systematic sample.
3.65 Systematic random samples versus simple random samples. The previous exercise introduces systematic random samples. Explain carefully why a systematic random sample does give every individual the same chance to be chosen but is not a simple random sample.
3.66 Random digit telephone dialing. An opinion poll in California uses random digit dialing to choose telephone numbers at random. Numbers are selected separately within each California area code. The size of the sample in each area code is proportional to the population living there.
AREACOD
(a) What is the name for this kind of sampling design?
(b) California area codes, in rough order from north to south, are
209 | 213 | 310 | 323 | 341 | 369 | 408 | 415 | 424 | 442 |
510 | 530 | 559 | 562 | 619 | 626 | 627 | 628 | 650 | 657 |
661 | 669 | 707 | 714 | 747 | 752 | 760 | 764 | 805 | 818 |
831 | 858 | 909 | 916 | 925 | 935 | 949 | 951 |
Another California survey does not call numbers in all area codes but starts with an SRS of eight area codes. Choose such an SRS. If you use Table B, start at line 132.
3.67 Select club members to go to a convention. A club has 30 student members and 10 faculty members. The students are
Abel | Fisher | Huber | Moran | Reinmann |
Carson | Golomb | Jimenez | Moskowitz | Santos |
Chen | Griswold | Jones | Neyman | Shaw |
David | Hein | Kiefer | O’Brien | Thompson |
Deming | Hernandez | Klotz | Pearl | Utts |
Elashoff | Holland | Liu | Potter | Vlasic |
and the faculty members are
Andrews | Fernandez | Kim | Moore | Rabinowitz |
Besicovitch | Gupta | Lightman | Phillips | Yang |
The club can send seven students and three faculty members to a convention and decides to choose those who will go by random selection. Select a stratified random sample of seven students and three faculty members.
3.68 Stratified samples for accounting audits. Accountants use stratified samples during audits to verify a company’s records of such things as accounts receivable. The stratification is based on the dollar amount of the item and often includes 100% sampling of the largest items. One company reports 5000 accounts receivable. Of these, 100 are in amounts over $50,000; 500 are in amounts between $1000 and $50,000; and the remaining 4400 are in amounts under $1000. Using these groups as strata, you decide to verify all of the largest accounts and to sample 5% of the midsize accounts and 1% of the small accounts. How would you label the two strata from which you will sample? Use software or Table B, starting at line 125, to select the first six accounts from each of these strata.
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3.69 The sampling frame. The list of individuals from which a sample is actually selected is called the sampling frame. Ideally, the frame should list every individual in the population, but in practice this is often difficult. A frame that leaves out part of the population is a common source of undercoverage.
(a) Suppose that a sample of households in a community is selected at random from the telephone directory. What households are omitted from this frame? What types of people do you think are likely to live in these households? These people will probably be underrepresented in the sample.
(b) It is usual in telephone surveys to use random digit dialing equipment that selects the last four digits of a telephone number at random after being given the area code and the exchange. The exchange is the first three digits of the telephone number. Which of the households that you mentioned in your answer to part (a) will be included in the sampling frame by random digit dialing?
3.70 Survey questions. Comment on each of the following as a potential sample survey question. Is the question clear? Is it slanted toward a desired response?
(a) “Some cell phone users have developed brain cancer. Should all cell phones come with a warning label explaining the danger of using cell phones?”
(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 escalating environmental degradation and incipient resource depletion, would you favor economic incentives for recycling of resource-intensive consumer goods?”