Part A.
Let's say you work for the Department of Social Services. You are asked to draw a sample of five clients and to mail them a questionnaire about their satisfaction with department services. You decide to draw a systematic sample with a random start.
A client list exists; it is found below. Answer the questions that follow the client list.
Able, John
Barnes, Karen
Barnes, Sheila
Barnes, Thomas
Carlson, Stephanie
Davis, Lucy
Eisman, Alice
Ferguson, Barbara
Goldwater, Elizabeth
Martin, Joyce
Naddle, Jill
Osterman, Steve
Patersen, Ingrid
Peterson, Willona
Plimpton, Susan
Stephens, Alice
Tomlinson, Tammy
Wilkerson, Robert
Williams, Christine
Zeiss, Brian
1. What is your sampling frame in this case?
2. What is your sampling interval?
3. Use the table of random numbers below to help you draw your sample. Circle the specific random number or numbers that you use. If you don't use all five digits of a number, circle the specific digits that you do use.
Random Number Table
62453 99214 33127 82542 76392 09124
38472 83203 98362 48298 83625 37262
27381 87394 28493 38477 39482 49275
93876 38271 38273 38471 38473 37384
48277 38272 39484 87276 38472 74728
4. On the list of names on the previous sheet (the list that goes from Able to Zeiss), circle the names of the people who fall into your systematic sample with a random start.
5. Briefly, describe below what you did to create this systematic sample.
Part B
1. Let's say that you have a sample of 400 people who have used the services of the Family Independence Agency of the State of Michigan during the last 10 years. The standard error = .025. What is the margin of error for this sample? (Assume the 95% confidence level.)
2. What is the confidence interval around the sample statistic (of 50%) for this sample? (Assume the 95% confidence level.)
3. What can you say about the POPULATION of people who have used the services of the Family Independence Agency when your SAMPLE says that 50% of clients (people who have used the services) are "satisfied" with services?