Is the sample proportion an unbiased estimator of the population proportion under a specified random-sampling model?
Conditions
- A specified random-sampling model is used.
- The estimator is the sample proportion.
- The target parameter is the population proportion.
Reasoning, step by step
- Identify the random-sampling model.
- Calculate the sample proportion for multiple repeated samples.
- Observe that the expected value of the sample proportion equals the population proportion.
- Note that in any finite simulation, the observed mean may deviate slightly from the true parameter.
Example
The script states: 'Under the specified random-sampling model, the sample proportion is unbiased for the population proportion. The observed mean of 35 estimates is close to 0.5 here; finite simulations need not match the parameter exactly.'
Common misconceptions
- Believing that the mean of a small number of sample proportions must exactly equal the population proportion.
- Confusing the property of unbiasedness (expected value) with the exact outcome of a finite simulation.
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