Can I get some assistance with this question? This problem uses a small population example to...
Can I get some assistance with this question?
This problem uses a small population example to compare the mean square error for using Hansen-Hurvtiz estimator versus the sample mean. The population consists of number of vacant seats of 4 airplanes. We only take a sample of size 1 to estimate the total number of vacant seats from these four airplanes.
|
airplane |
A |
B |
C |
D |
|
size |
40 |
60 |
100 |
300 |
|
Vacant seats |
9 |
12 |
23 |
63 |
- Compute the MSE when you take a srs of size 1.
- Compute the MSE when you sample with probability proportional to size and use the Hansen-Hurvitz estimator.
Homework Answers
We just make use of the fact that for any estimator T, its MSE is the sum if its variance and the square of bias.
Since the HH estimator takes into account the size measures, it captures a better picture of the population and hence has lower MSE than the corresponding UE of population total under SRS sampling scheme.
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