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Which of the following best describes the condition necessary to justify using a pooled estimator of the population variance?
1- Assuming this represents a random sample from the population, the sample mean is an unbiased estimator of the population mean. 2-Because they are robust, t procedures are justified in this case. 3- We would use z procedures here, since we are interested in the population mean.
Why median is not a consistent estimator?
Because it is easily influenced by extreme values (i.e. it is not unbiased).
What is an unbiased estimator?
An unbiased estimator is a person who gives a price for a service or goods and that person has no ulterior motives that would influence the price either way. A person who is biased might reflect the estimated price to show favor to one person more than another. For example: If my uncle was to bid on a job and I was the estimator for the person who wanted the work done, then I would have a bias in that I would reflect the price so that my uncle would get the job. This is unethical and illegal. An unbiased person has no preference as to who would get the job and would do the estimate honestly. An unbiased estimator has a very specific meaning in statistics and a good statistician needs to answer this meaning of the term.
What is the uses of ratio estimator?
what is the use and application of ratio estimator?
How large would your sample have to be for appropriate estimation of the whole population?
First you have chose an estimator for what you want to know about the population. In general the level of variability in the result that any estimator provides will depend on the variability in the population. Therefore, the greater the variability in the population the larger your sample size must be. You will also need to decide how much precision is required in your estimate. The more precision you require the greater your sample size will have to be.
Why is the sample mean an unbiased estimator of the population mean?
The sample mean is an unbiased estimator of the population mean because the average of all the possible sample means of size n is equal to the population mean.
What is the best estimator of population mean?
The best estimator of the population mean is the sample mean. It is unbiased and efficient, making it a reliable estimator when looking to estimate the population mean from a sample.
Is sample variance unbiased estimator of population variance?
No, it is biased.
What is the proof that demonstrates the unbiased estimator of variance?
The proof that demonstrates the unbiased estimator of variance involves showing that the expected value of the estimator equals the true variance of the population. This is typically done through mathematical calculations and statistical principles to ensure that the estimator provides an accurate and unbiased estimate of the variance.
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.
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 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.
Which of the following best describes the condition necessary to justify using a pooled estimator of the population variance?
1- Assuming this represents a random sample from the population, the sample mean is an unbiased estimator of the population mean. 2-Because they are robust, t procedures are justified in this case. 3- We would use z procedures here, since we are interested in the population mean.
Differentiate estimate and estimator?
It can get a bit confusing! The estimate is the value obtained from a sample. The estimator, as used in statistics, is the method used. There's one more, the estimand, which is the population parameter. If we have an unbiased estimator, then after sampling many times, or with a large sample, we should have an estimate which is close to the estimand. I will give you an example. I have a sample of 5 numbers and I take the average. The estimator is taking the average of the sample. It is the estimator of the mean of the population. The average = 4 (for example), this is my estmate.
Meaning of BLUE in least square?
Best Linear Unbiased Estimator.
Why median is not a consistent estimator?
Because it is easily influenced by extreme values (i.e. it is not unbiased).
What is an unbiased estimator?
An unbiased estimator is a person who gives a price for a service or goods and that person has no ulterior motives that would influence the price either way. A person who is biased might reflect the estimated price to show favor to one person more than another. For example: If my uncle was to bid on a job and I was the estimator for the person who wanted the work done, then I would have a bias in that I would reflect the price so that my uncle would get the job. This is unethical and illegal. An unbiased person has no preference as to who would get the job and would do the estimate honestly. An unbiased estimator has a very specific meaning in statistics and a good statistician needs to answer this meaning of the term.
