EXAM I FR 3218/5218 Semester II - 2003

If it is not clear what a question is asking, request clarification from the instructor. Misreading a question is not grounds for partial credit. To receive partial credit for the calculation problems, formulas and intermediate calculations must be legibly shown. A good strategy would be to go through and answer/set up as much of each calculation question as you can and then go back to fill in details. It is my experience that divine intervention seldom occurs during examinations.

The number preceding the question number is the point value of that particular question. Any number of multiple-choice options (including zero) may be correct responses to the question statement; circle all correct responses. Total points = 34.

(3) 1. Identify what information is needed when you set out to PLAN a sample survey. I am looking for three key items; you may list more than three.

(2) 2. Systematic selection of sample units is commonly used in forest inventory sampling applications. Why is this the case when most statisticians warn against the use of systematic sampling?

(5) 3. Sixty (60) lakes in Itasca County are of interest due to high potential of winter fish kill. You are in charge of selecting a simple random sample of lakes (without replacement) to determine the actual extent of the problem this year. Measuring oxygen content of lake water assesses the extent of the problem. From surveys in past years, the coefficient of variation of oxygen content observations (lake to lake variation) has averaged 50 percent. You are told to obtain an estimate of mean oxygen content of lakes with a standard error no larger than 10 percent of the mean. How many lakes will be in your sample?

(5) 4. An unequal probability sample (probability proportional to size) of two units is selected from the following population of six units based on the random numbers 100 (first unit selected) and 150 (second unit selected). The observed values of the variable of interest were 20 (first unit selected) and 40 (second unit selected).

a. Which units (unit numbers) were actually selected?

b. What is the unequal probability sampling estimate of MEAN PER UNIT?

Unit Number	Unit Size	Unit Number	Unit Size
1	50	4	10
2	20	5	50
3	40	6	30

(4) 5. What factor or factors determine the degree to which a well-designed stratified random sample improves upon (has a lower standard error than) a simple random sample?

a. differences in stratum sizes

b. differences in stratum means

c. differences in stratum standard deviations

d. differences in stratum variances

(6) 6. Given the following summary statistics from a stratified simple random sample, compute a 90% confidence interval for the population mean. Use the attached Student’s-t table.

Stratum	Total Units in Stratum	Units Sampled in Stratum
1	50	20	10	5
2	150	10	5	2

(4) 7. In regression/ratio sampling (m_x known), the estimators differ in that:

a. the regression estimator will always produce a greater adjustment

b. the ratio estimator adjusts in an additive manner

c. only the ratio estimator adjusts both the mean and the total

d. only the regression estimator directly adjusts

(5) 8. Interest lies in the seed crop of a seed orchard of 500 coniferous trees for a particular year (a seed orchard is a stand of trees maintained for the production of seed; a coniferous tree is one where seeds are in cones). Number of cones per tree is known to be linearly related to (tree crown radius)². Describe how you might use double sampling with a regression or ratio estimator to assist in estimating the amount of seed this seed orchard will produce in the particular year. Identify what assumption you might want to make about number of seeds per cone.