Exam 1                                                 FR 3218/5218                                 Semester II, 2006

 

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. Total points = 78.

 

(10) 1. Identify/define the sampling frame you would use if interest lie in number of walleye caught on the opening day of walleye fishing season in Minnesota; defend your choice if you see alternatives. What’s your sample unit and what will you observe? How will you observe it? Do you see potential for any problems? (note – I AM NOT asking for what sampling technique you would use; further, there is no single correct answer)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(12) 2. (homework 2, 1d.)You are to use simple random sampling without replacement to sample a population of size 100 units. You wish to achieve a standard error of 8 percent. You have little idea about variability in the population but you suspect values on the variable of interest probably range from 10 to 30. Your college textbook claims that a reasonable estimate of stand deviation (Sy) is (range/4) and you know that the mid-range provides an estimate of population mean. What size sample should you take to achieve the desired standard error?

 

(if you are unable to use the range information to answer the question, you may, for some loss of credit, just assume a population coefficient of variation of 30%)

 

 

 

 

 

(10) 3. (homework 2, 1f.)You wish to estimate the proportion of households in St. Paul that have garbage disposals (AKA rat feeders) in their kitchen sinks. You take a simple random sample with replacement of 100 houses and find that 20 have garbage disposals in their kitchen sinks (that is you have 20 observations of “1” and 80 observations of “0”). Provide a 95% confidence interval on the true proportion of households in St. Paul that have garbage disposals in their kitchen sinks. (if you get stuck on some part of this question, forge ahead by making assumptions, i.e. try to work through the whole problem)

 

 

 

 

 

 

 

 

(16) 4. Explain what needs to be true, what extra information do we need to possess, for each of the following sampling techniques to give us a more reliable estimate (smaller standard error) of the population mean than simple random sampling for the same amount of time/money spent.

 

i.                     systematic sampling

 

 

 

 

 

ii.                   unequal probability sampling

 

 

 

 

 

iii.                  stratified random sampling

 

 

 

 

 

iv.                 regression estimation (with a random sample)

 

 

 

 

 

(10) 5. (homework 3, 2.) We are going to take a total sample size of 100 units (no more, no less) from a population consisting of two strata. Given the following information:

 

Stratum            Nh        Sh2

---------                       ----      ----

     1                 200      400

     2                 600      100

 

how will we allocate the 100 units to the strata under:

 

i.                     proportional allocation

 

 

ii.                   optimal allocation with equal costs

 

 

 

 

 

(12) 6. (homework 3, 3.) The Excel worksheet printout on the following page summarizes data collected using a random sample where regression or ratio estimation was to be used. It is known that the true mean per unit of X for the population is 75.

 

i. What is the regression estimate of population mean per unit of Y?

 

 

 

ii. What is the ratio-of-means estimate of population mean per unit of Y?

 

 

 

iii. Which of the two estimates is likely more appropriate given underlying assumptions? Explain.

 

 

 

 

(8) 7. What requirement of each of the following sampling methods does using double sampling in conjunction with the method do away with?

 

i.                     stratified random sampling

 

 

 

ii.                   random sampling with a regression/ratio estimator