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 random sample of 400 people who have used the services of the Department of Human Services of the State of Michigan during the last 10 years. What is the standard error for this sample?
2. What is the sampling error (margin of error) for the sample discussed in Question 1, assuming that you want to be 95% confident?
3. What is the sampling error (margin of error) for the sample discussed in Question 1, assuming that you want to be 99% confident?
4. Let's assume that you have a probability sample of 1,000 Michiganders. 58% say that they favor Jennifer Granholm for Governor. What is the confidence interval around the sample statistic for this sample? (Assume the 95% confidence level.)
5. What can you say about the POPULATION of people in Michigan, given the confidence interval that you created for Question 4?
6. If the average number of children people have in a random sample of 2,000 people is 2.1 and the standard deviation is 1.2, what is the standard error?
7. Given the data in Question 6, what is the margin of error if you want to be 95% confident?
8. Given the data in Question 7, what is the confidence interval around the mean if you want to be 95% confident?
9. What does the confidence interval tell you about the average number of children people in the population have?