SECTION 3.2 Exercises

For Exercises 3.17 and 3.18 see page 130; for 3.19 and 3.20, see pages 131–132; for 3.21 and 3.22, see page 134; for 3.23 and 3.24, see page 136; and for 3.25, see page 138.

Question 3.26

3.26 What’s wrong?

Explain what is wrong in each of the following statements.

  1. A simple random sample is the only way to randomly select cases from a population.
  2. Random digits cannot be used to select a sample from a population that has more than 100 cases.
  3. The population consists of all cases selected in a simple random sample.

Question 3.27

3.27 What’s wrong?

Explain what is wrong with each of the following random selection procedures, and explain how you would do the randomization correctly.

  1. To determine the reading level of an introductory statistics text, you evaluate all of the written material in the third chapter.
  2. 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.
  3. 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.

3.27

(a) Material from the third chapter is likely not representative of the reading level for the entire book. One example of how to randomize is to randomly select pages and evaluate the reading level of these. (b) Students who attend a particular class at 7:30 a.m. are certainly not representative of all students. A list of all students needs to be used in which you randomly selected 100 to participate. (c) Taking subjects from the top or bottom of an alphabetized list gives different chances of being selected that taking subjects based on the first letter of their name and is not equally likely. Using number assignments and random digits is an appropriate selection process.

Question 3.28

3.28 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 120 businesses at random. Of these, 54 return the questionnaire mailed by the committee. What is the population for this sample survey? What is the sample? What is the rate (percent) of nonresponse?

Question 3.29

3.29 Popularity of news personalities can affect market share.

A Gallup Poll conducted telephone interviews with 1001 U.S. adults aged 18. One of the questions asked whether the respondents had a favorable or an unfavorable opinion of 17 news personalities. Diane Sawyer received the highest rating, with 80% of the respondents giving her a favorable rating.18

  1. What is the population for this sample survey? What was the sample size?
  2. The report on the survey states that 8% of the respondents either never heard of Sawyer or had no opinion about her. When they included only those who provided an opinion, Sawyer’s approval percent rose to 88%, and she was still at the top of the list. Charles Gibson, on the other hand, was ranked eighth on the original list, with a 55% favorable rating. When only those providing an opinion were counted, his rank rose to second, with 87% approving. Discuss the advantages and disadvantages of the two different ways of reporting the approval percent. State which one you prefer and why.

141

3.29

(a) The population is all U.S. adults aged 18. The sample size is 1001. (b) Including all the respondents gives a better perspective of the popularity or reputation of the person. Excluding the respondents who have never heard of them or had no opinion gives a better perspective of what we might call their “likeability” (either in terms of their persona or the quality of their news reports).

Question 3.30

3.30 Identify the populations.

For each of the following sampling situations, identify the population as exactly as possible. That is, indicate what kind of cases the population consists of and exactly which cases fall in the population. If the information given is not complete, complete the description of the population in a reasonable way.

  1. 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.
  2. The American Community Survey (ACS) replaced the census “long form” starting with the 2010 census. The main part of 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.
  3. 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?”

Question 3.31

3.31 Interview potential customers.

You have been hired by a company that is planning to build a new apartment complex for students in a college town. They want you to collect information about preferences of potential customers for their complex. Most of the college students who live in apartments live in one of 33 complexes. You decide to select six apartment complexes at random for in-depth interviews with residents. Select a simple random sample of six of the following apartment complexes. If you use Table B, start at line 107.

resid

Ashley Oaks Burberry Del-Lynn
Bay Pointe Cambridge Fairington
Beau Jardin Chauncey Village Fairway Knolls
Bluffs Country Squire Fowler
Brandon Place Country View Franklin Park
Briarwood Country Villa Georgetown
Brownstone Crestview Greenacres
Lahr House Peppermill Salem Courthouse
Mayfair Village Pheasant Run Village Manor
Nobb Hill Richfield Waterford Court
Pemberly Courts Sagamore Ridge Williamsburg

3.31

The complexes selected are 20, 11, 31, 07, 24, and 17.

Question 3.32

3.32 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 200 pixels. For a random sample of 30 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 152 and choose only the first six pixels in the sample.

Question 3.33

3.33 Select a simple random sample.

After you have labeled the cases 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.

Question 3.34

3.34 Select a simple random sample.

There are approximately 446 active telephone area codes covering Canada, the United States, and some Caribbean areas.19 (More are created regularly.) You want to choose an SRS of 30 of these area codes for a study of available telephone numbers. Use software or the Simple Random Sample applet to choose your sample.

acodes

Question 3.35

3.35 Repeated use of Table B.

In using Table B repeatedly to choose samples, you should not always begin at the same place, such as line 101. Why not?

3.35

If the same set of random digits is used, then the process is no longer random.

Question 3.36

3.36 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 four addresses out of 100. Because , we can think of the list as four lists of 25 addresses. Choose one of the first 25 at random, using Table B. The sample contains this address and the addresses 25, 50, and 75 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, and 88.

  1. A study of dating among college students wanted a sample of 200 of the 9000 single male students on campus. The sample consisted of every 45th name from a list of the 9000 students. Explain why the survey chooses every 45th name.
  2. Use software or Table B at line 135 to choose the starting point for this systematic sample.

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Question 3.37

3.37 Systematic random samples versus simple random samples.

The previous exercise introduces systematic random samples. Explain carefully why a systematic random sample does give every case the same chance to be chosen but is not a simple random sample.

3.37

Call the initial number chosen the “leading” number. All numbers form groups based off their leading number. Certainly, each leading number has an equal chance of being selected. Then, for each subsequent number, it is automatically chosen if its leading number is chosen. Which means all numbers (a.k.a. all groups) have an equal chance to be chosen. It is not a simple random sample because certain numbers can’t be chosen together, so all possible samples are not possible, only the pre-formed groups based off leading numbers.

Question 3.38

3.38 Random digit telephone dialing for market research.

A market research firm 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.

  1. What is the name for this kind of sampling design?
  2. California area codes, in rough order from north to south, are
209 213 310 323 408 415 510 530 559 562
619 626 650 661 707 714 760 805 818 831
858 909 916 925 949

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.

cacodes

Question 3.39

3.39 Select employees for an awards committee.

A department has 30 hourly workers and 10 salaried workers. The hourly workers 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 salaried workers are

Andrews Fernandez Kim Moore Rabinowitz
Besicovitch Gupta Lightman Phillips Yang

The committee will have seven hourly workers and three salaried workers. Random selection will be used to select the committee members. Select a stratified random sample of seven hourly workers and three salaried workers.

cmemb

Question 3.40

3.40 When do you ask?

When observations are taken over time, it is important to check for patterns that may be important for the interpretation of the data. In Section 1.2 (page 19), we learned to use a time plot for this purpose. Describe and discuss a sample survey question where you would expect to have variation over time (answers would be different at different times) for the following situations:

  1. Data are taken at each hour of the day from 8 A.M. to 6 P.M.
  2. Date are taken on each of the seven days of the week.
  3. Data are taken during each of the 12 months of the year.

Question 3.41

3.41 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?

  1. “Some cell phone users have developed brain cancer. Should all cell phones come with a warning label explaining the danger of using cell phones?”
  2. “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?”
  3. “In view of escalating environmental degradation and incipient resource depletion, would you favor economic incentives for recycling of resource-intensive consumer goods?”

3.41

(a) The first sentence is slanted toward yes because it suggests a possible link between cell phones and brain cancer. (b) The question is slanted toward agreeing because it starts “Do you agree … ” and also contains a possible advantage of “reduce administrative costs.” (c) This is slanted toward a favorable response by the phrases “escalating environmental degradation” and “incipient resource depletion.”