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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.
How much error between sample mean and population mean?
The answer depends on the underlying variance (standard deviation) in the population, the size of the sample and the procedure used to select the sample.
The sample variance is always smaller than the true value of the population variance is always larger than the true value of the population variance could be smaller equal to or?
yes, it can be smaller, equal or larger to the true value of the population varience.
When using the distribution of sample mean to estimate the population mean what is the benefit of using larger sample sizes?
The variance decreases with a larger sample so that the sample mean is likely to be closer to the population mean.
Can the variance of a sample be negaTIve?
No.
If a sample of 66 employees were taken from a population of 820 employees s2 could refer to the variance of how many of the employees salarues?
In this context, ( s^2 ) would refer to the sample variance of the salaries of the 66 employees taken from the population of 820 employees. It is a measure of how much the salaries of these sampled employees deviate from their average salary. This sample variance provides an estimate of the variance of the population, assuming that the sample is representative.
Why the sample variance is an unbiased estimator of the population variance?
The sample variance is considered an unbiased estimator of the population variance because it corrects for the bias introduced by estimating the population variance from a sample. When calculating the sample variance, we use ( n-1 ) (where ( n ) is the sample size) instead of ( n ) in the denominator, which compensates for the degree of freedom lost when estimating the population mean from the sample. This adjustment ensures that the expected value of the sample variance equals the true population variance, making it an unbiased estimator.
What is the proof that the sample variance is an unbiased estimator?
The proof that the sample variance is an unbiased estimator involves showing that, on average, the sample variance accurately estimates the true variance of the population from which the sample was drawn. This is achieved by demonstrating that the expected value of the sample variance equals the population variance, making it an unbiased estimator.
What does it mean to say that the sample variance provides an unbiased estimate of the population variance?
It means you can take a measure of the variance of the sample and expect that result to be consistent for the entire population, and the sample is a valid representation for/of the population and does not influence that measure of the population.
Is sample variance unbiased estimator of population variance?
No, it is biased.
How do you prove that the sample variance is equal to the population variance?
You cannot prove it because it is not true.The expected value of the sample variance is the population variance but that is not the same as the two measures being the same.
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.
Is there a proof that demonstrates the unbiasedness of the sample variance?
Yes, there is a mathematical proof that demonstrates the unbiasedness of the sample variance. This proof shows that the expected value of the sample variance is equal to the population variance, making it an unbiased estimator.
What does n-1 indicate in a calculation for variance?
The n-1 indicates that the calculation is being expanded from a sample of a population to the entire population. Bessel's correction(the use of n − 1 instead of n in the formula) is where n is the number of observations in a sample: it corrects the bias in the estimation of the population variance, and some (but not all) of the bias in the estimation of the population standard deviation. That is, when estimating the population variance and standard deviation from a sample when the population mean is unknown, the sample variance is a biased estimator of the population variance, and systematically underestimates it.
What is n-1in statistics?
In statistics, "n-1" refers to the degrees of freedom used in the calculation of sample variance and sample standard deviation. When estimating variance from a sample rather than a whole population, we divide by n-1 (the sample size minus one) instead of n to account for the fact that we are using a sample to estimate a population parameter. This adjustment corrects for bias, making the sample variance an unbiased estimator of the population variance. It is known as Bessel's correction.
How much error between sample mean and population mean?
The answer depends on the underlying variance (standard deviation) in the population, the size of the sample and the procedure used to select the sample.
The sample variance is always smaller than the true value of the population variance is always larger than the true value of the population variance could be smaller equal to or?
yes, it can be smaller, equal or larger to the true value of the population varience.
