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Show that in simple random sampling the sample variance is an unbiased estimator of population variance?
It is a biased estimator. S.R.S leads to a biased sample variance but i.i.d random sampling leads to a unbiased sample variance.
What is the definition for unbiased sample?
A sample is Unbiased if everyone in the sample have an equal chance of being selected
What biased estimator will have a reduced bias based on an increased sample size?
The standard deviation. There are many, and it's easy to construct one. The mean of a sample from a normal population is an unbiased estimator of the population mean. Let me call the sample mean xbar. If the sample size is n then n * xbar / ( n + 1 ) is a biased estimator of the mean with the property that its bias becomes smaller as the sample size rises.
Advantages of census over sample survey?
It is more accurate, unbiased and includes every item in the population, whereas sampling may be biased, and sampling is not totally representative.
Is a sample UNBIASED?
Only if you make it unbiased. Samples can be weird. If you make it unbiased, then yes.
