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.

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.

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.

3.53 Interview some students. Refer to the previous exercise.

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.

3.55 What’s wrong? Explain what is wrong in each of the following scenarios.

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.

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.

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.

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.

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.

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.

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.

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

and the faculty members are

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.

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.

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?