1. Assign a number to each member of class. Use a random number table to draw a random sample of five students from class. Does your sample appear to be representative?  (gender, hair color, row...)

2. What proportion of the two-digit random numbers did you use?  What proportion did you disregard?  Can you think of a more efficient way to assign the two digit random numbers to students?

3.  Use the random number generator on you calculator to draw a random sample of five students from the class.
MATH-->PRB-->randInt (lower bound, upper bound, # of samples).

4. Which of the following sampling methods produce a random sample from a class of 36 students?
 a. Select the first six students to enter a room.

 b. Select those students whose phone numbers end with the digit 4.

 c. Suppose that the class has 18 boys and 18 girls.  Select a sample of 6 students by using a random number table to choose 1 of the 18 boys, then 1 of the 18 girls, then a boy, then a girl, and so on until you have chosen 6 students.

 d. Suppose that the classroom has six rows of chairs with six chairs in each row.  Assign the rows the digits 1 through 6.  Throw a die and place all the students in the row corresponding to the number on the die in the sample.

 e. Assign each student a number from 1 to 36.  The girls get the number 1 to 18 and the boys the numbers from 19 to 36, and place the corresponding students in the sample.

5. For each sampling method below, tell which groups in the population are likely to be underrepresented.
 a. To obtain a sample of households, a television rating service dials numbers taken at random from telephone directories.

 b. In 1984, Ann Landers conducted a poll on the marital happiness of women by asking women to write to her.

 c. To determine the percentage of teenage girls with long  hair, Teen magazine published a mail-in questionnaire.  Of the 500 respondents, 85% had hair shoulder length or longer (USA Today, July 1, 1985).

 d. To evaluate the reliability of cars owned by its subscribers, Consumer Reports magazine publishes a yearly list of automobiles and their frequency-of-repair records.  The magazine collects the information by mailing a questionnaire to subscribers and tabulating the results from those who return it.

 e. A college psychology professor needs subjects for a research project to determine which colors average American adults find restful.  From the list of all 743 students taking introductory psychology at her school, she selects 25 students using a random number table.

 f. For a survey of student opinions about school athletic programs, a member of the school board obtains a sample of students by listing all students in the school and using a random number table to select 30 of them.  Six of the students say that they don't have time to participate, and they are eliminated from the sample.

6. If a sample of 20 adults ends up containing only men, two explanations are possible.  The first is that the sampling procedure wasn't random; the second is that the sampling procedure was random but that a nonrepresentative sample resulted.  Which explanation would you be more inclined to believe?  Explain.

7. Repeat question 6 but assume that the sample of size 20 had 13 men.

8. Describe how you could actually obtain a sample of 30 students from the population of students in your school using the following methods.
 a. random sampling                                                        b. convenience sampling

 c. sampling by self-selection                                           d. stratified random sampling
 
 e. systematic sampling                                                    f. cluster sampling

9. Retailers at the Logan Mall want to survey their Saturday customers about their satisfaction with the eating facilities within the mall. One merchant went to business school and learned about the importance of statistics, so he wants to obtain a random sample.  He proposes the following method: Interviewers should stand at the center of the mall and select the first 100 people who walk by after 11:00 a.m.  He believes this approach will provide a random sample because the interviewers will not exercise any decision over whether or not ot include specific individuals in the sample.
 a. What kind of sample would the merchant really get?

 b. In what way might this sampling method be biased?

 c. Describe how the merchant could modify this approach to use a version of systematic sampling.

 d. If the retailer were to use stratified random sampling, what strata would you recommend that he choose?

10. The Educational Testing Service (ETS) needed a representative sample of college students.  ETS first divided all colleges into groups of similar ones (such as public colleges with more than 25,000 students, small private schools, and so on). Then they used their judgement to choose one representative school from each group, thus obtaining the sample of schools.  Each school in turn picked a sample of students.
 a. ETS divided the colleges into strata but did not perform stratified random sampling. Explain.

 b. Suggest ways to improve this sampling scheme.

11. Researchers wanted a representative sample of Japanese-Americans living in San Francisco.  "The procedure was as follows.  After consultation with representative figures in the Japanese community, the four most representative blocks int the Japanese area of the city were chosen; all persons resident in those four blocks were taken for the sample.  However, a comparison with Census data shows that the sample did not include a high-enough proportion of Japanese with college degrees".
 a. What kind of sampling did this study use?

 b. Why do you suppose the sample did not have enough college graduates?
 
12. The headline on page 11 of an Illinois newspaper stated, "More people using drugs at work, survey reports."  The article gave the following information: "The survey questioned 227 people who called the national [cocaine] helpline, chosen at random, during a six-week period in February and March...Ninety-two percent of the callers said they sometimes worked while under the influence of drugs" (Rockford Register Star, March 25, 1985).
 a. What kind of sampling was used?

 b. What population would you say this sample was drawn from?

 c. Describe why this survey does not justify the claim made in the headline.