FINAL TEST STA4222/5225 SPRING, 2000 D.A. MEETER

Due: April 25, 9 A.M. I have not given or received aid from other humans on this exam.

Questions in bold are extra credit for STA 4222 Name:_____________________________

The state of Florida wants to survey the energy use of all dwelling units (du). There are 5,000,000 du's served by 50 utilities. The per-utility numbers of du's are (in thousands) 10, 12, 12.5, 13, ... , 62, 67, 78, 80, 400, 450, 900, 1,300. A sample of n = 1000 is desired. Consider plans A-F:

2. Obtain a list of all du's from each electric utility; combine these lists. Select an srs of pages

from the list; each page has 80 entries. Select four entries at random from each page.

3. Obtain a list of all du's from each electric utility; combine these lists. Select an srs of pages from the list; take all entries on the page; each page has 80 entries.
4. Take a separate srs sample in each county; choose different n's in each county based on cost and

variance within county.

5. Take a separate srs in every utility, not all with the same f.

F. Select 10 utilities at random and select a constant fraction (f) from each utility.

I. TYPES OF PLANS

For each plan above, give the number of the best description.

1. srs

2. systematic selection

3. quota

4. stratified

5. proportionate stratified

6. post-stratified

7. optimally stratified

8. cluster

9. two-stage sampling, equal clusters

10. two-stage sampling, unequal clusters

11. stratified clustered

12. stratified clustered with subsampling

II. PLAN DETAILS

1. Which plan would be expected to have a larger variance, B or C? Why?

2. What is unsatisfactory about plan F? State two methods of dealing with this problem which

could be useful in this case.

3. In Plan C, describe population, sampling unit, element, frame.

4. In Plan A, calculate k and state the possible values of r.

5. The standard deviation of the estimator in Plan F is 2.5 times larger than that of the srs. How many observations need to be taken to get the same precision as an srs of 1000?

III. SYSTEMATIC SELECTION

In each case, state what problems (if any) might be caused by using systematic selection on the frame. DO NOT question the FRAME.

1. Republican Women's Club. The membership roster is ordered by year of joining the club. Questions involve opinions on issues.

2. Big Bend Sierra Club. The list is alphabetical by last name. Questions involve priorities on ecological issues.

3. Boy Scouts of Leon County. The list is sorted by troop; each troop is about the same size, and within each troop, the members are grouped by rank. Generally, older scouts have higher rank. Questions involve satisfaction with scouting.

IV. CLUSTER SAMPLING

In each case, what concerns (if any) could be caused by cluster sampling. DO NOT question the FRAME.

1. Boy Scouts again. Each cluster is a troop. The questions involve satisfaction with scouting.

3. Department of Insurance rate increase filings. A cluster is all filings received in a week. Y = time to process a filing.

5. RATIO, REGRESSION, AND DIFFERENCE ESTIMATION

1. FSU undergraduates. Y = GPA, X = SAT score. Ratio estimation

2. Y = votes cast in a precinct, X = number of voters registered there. Regression.

3. Y = 1999 incidents of school violence/state, X = 1998 data. What form of estimation? Why?

VI. Questionnaires involving opinions about musical events are to be given to attendees at events with ticket charges in the FSU School of Music; n = 1000. The events, maximum nightly capacity in ( ), are eight opera performances (1,200), four orchestra concerts (1,200), six chamber concerts (500), and 10 recitals(200). Describe sampling plan, population, frame, element, sampling unit. Justify your plan in terms of cost/variance, ease of execution by music school employees, and good response rate.