1. A researcher plans a study of housing quality of low-income households in Y County, CA. He needs a sample of 500 households to accomplish his purpose. He ascertains from the Y county Housing Authority that there are 5,000 households living in public housing (requiring low income for eligibility) in the county. He obtains a list of these households' names and addresses, numbers them from 1 to 5,000, and chooses 500 of these households using a computer-generated list of random numbers. He tries to collect data from these 500 households via a mailed questionnaire.

a. To what population does this researcher wish to generalize?

b. What is the sampling frame in this study?

c. What type of sampling does this researcher do (be precise)?

d. Describe the chance that each household in the sampling frame has of ending up in the sample.

e. How well does this sampling frame reflect his stated population? Why?

f. What could he do if he wanted to improve the external validity of the research?

2. A researcher wants to study L.A. public university seniors' career choices and plans to collect data from CSUN, UCLA, and CSULA. The researcher receives permission to use the registration records on the three campuses. CSUN has 8,000 seniors, UCLA has 10,000 seniors, and CSULA has 5,000 seniors. He needs 500 seniors in his study, so on each campus's list, he randomly picks a name to start with and then selects each rth senior on the list until he has 500 seniors drawn.

a. What is the theoretical population to which the researcher wishes to generalize?

b. What is the accessible population in this study?

c. What type of sampling plan does this study utilize (be precise)?

d. What is the value of r in that the researcher should use (show your work)?

e. What is the number of seniors that will be obtained from each campus?

f. Describe the chance that each senior has of ending up in this sample.

g. What is the advantage of this sampling plan over a simple random sampling plan?

h. What must this researcher ascertain before he can be reasonably confident that using this sampling plan will produce a representative sample?

3. A researcher wishes to investigate health conditions of the elderly (aged 65+) householders in Z County, CA. Previous research suggests that elders' place of residence (metro (a.k.a. urban) versus non-metro (rural)) is an important variable affecting their health conditions. So, in 2008 from a county map, she randomly selects census tracts , of which the county has 155 (100 metro and 55 non-metro as defined in the U.S. Census Bureau 2000 census). She selects 10% of the "metro" tracts and 10% of the "non-metro" tracts. Data collectors are sent to each selected tract and instructed to interview each eligible householder within each tract until they all have been interviewed.

a. What is the theoretical population to which this researcher wishes to generalize?

b. What is the sampling frame in this study?

c. What type of sampling plan does this researcher utilize (be precise)?

d. Describe the chance each elderly householder in this county has of ending up in the sample.

e. In your opinion, are there any problem(s) of the sampling plan?

4. Researchers wanted a sample of a state's population of two-parent families with exactly two children under 18 years old. An important variable in their study was age of the younger child in the family. The state has 100 counties; they randomly selected 5 of these from the list of the state's counties. They conducted a school census in these 5 counties, in which they measured the number of parents in each child's home, the number of children, and the ages of the children in the family. They retained only those children who had exactly two parents and one sibling. They divided families into groups that had younger children of five different ages: under 1, one year old, 2-5 years old, 5-11 years old, and 12-17 years old. Each of these lists had a different number of families. They randomly selected 42 of the families on each list (for a total sample of 210 families).

a. What was the theoretical population to which the researchers wanted to generalize?

b. What were the sampling frames in this study?

c. What type of sampling did they use (describe it as completely as possible)?

d. What is the age of the younger child variable called?

e. Why do you think these researchers did not plan a simple random sampling plan?

5. A team of researcher wants to analyze the incidence of unresolvable car repair complaints among California consumers in the past 12 months. They contact the California Department of Consumer Affairs and obtain a list of the problems that CA consumers complained to their office about in the past 12 months. They divide the complaints into those that relate to automobile repairs and all others. Then they use the automobile repair complaints as their sample.

a. What type of sampling do these researchers use?

b. Evaluate the external validity of this sampling plan, given the researchers' purpose.