EXAM I     FR 3218/5218             Semester II - 2002

 

 

            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 = 38.

 

(2) 1. Both observations and estimators have variances. The square root of the variance of observations is usually called standard __________ . The square root of the variance of an estimator is usually called standard __________ .

 

(4) 2. One chooses to use simple random sampling:

a.       when no prior knowledge exists concerning the population of interest

b.      to ensure one doesn’t get a non-representative or “bad” sample

c.       because it is defensible statistically

d.      to maximize cost efficiency

 

(5) 3. You are going to sample (with random sampling) a 10-acre stand with replacement for cordwood volume. Based upon prior experience, your best guesses at mean cords per acre and variance of observations are 20 and 100, respectively. How many sample units would be required to obtain an estimate of mean cords per acre with a standard error of 2 cords per acre?

 

 

 

 

 

 

 

 

 

(4) 4. The population of size N=6 units shown below is to be sampled with probability proportional to size (and with replacement). Based on the presentation in class:

i.              identify the random integers that would lead to selection of unit 3

 

ii.             compute the probability of selecting unit 3

 

 

              

Unit         Size               Unit               Size

1             17               4               13

2             8               5               22

3             35               6               20

 

 

 

(4) 5. In stratified sampling, strata are formed such that:

a.       variability within a stratum is minimal

b.      variability among strata is minimal

c.       units within a stratum are equal size

d.      travel costs within a stratum are equal

 

(6) 6. Given the following summary statistics from a stratified simple random sample, compute a 95% confidence interval for the population total. Assume Student’s-t = 2.

 

Stratum

Total Units in Stratum

Units Sampled in Stratum

Sample Mean

Variance of Sample Mean

1

400

10

20

4

2

200

5

50

100

 

 

 

 

 

 

 

 

 

 

(3) 7. In regression/ratio sampling (as we discussed it) one chooses among three possible estimators (regression, ratio-of-means, mean-of-ratios) by first validating that Y and X have a _________ relationship and then observing:

 

            i.

 

            ii.

(4) 8. Double sampling with a regression estimator differs from regression sampling in that regression sampling:

a.       involves selection with unequal probability

b.      requires N be known

c.       cannot be used in conjunction with stratification

d.      assumes a known intercept

 

(4) 9. Double sampling with a ratio-of-means estimator was used to estimate volume per hectare in a large Scots pine forest. From 100 aerial-photo-based plots, volume was estimated to be 280 m3/ha. From 20 ground plots, volume was estimated to be 240 m3/ha.; for those 20 plots aerial-photo-based volume was estimated to be 350 m3/ha. What is the ratio-of-means estimate of volume per hectare?

 

 

 

 

 

 

 

(2) 10. What are the purposes of the two samples in a double sampling for stratification design (i.e. what is observed in each sample or phase and why)?