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Yes, the sample mean is an unbiased estimator of the population mean. This means that, on average, the sample mean will equal the true population mean when taken from a large number of random samples. In other words, as the sample size increases, the expected value of the sample mean converges to the population mean, making it a reliable estimator in statistical analysis.
What else can I help you with?
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.
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.
Why in the case of population is n and in sample is n-1?
In statistics, when calculating variance or standard deviation for a population, we use ( n ) (the total number of observations) because we have complete data. However, for a sample, we use ( n-1 ) (the degrees of freedom) to account for the fact that we are estimating a population parameter from a sample. This adjustment helps to correct for bias and provides a more accurate estimate of the population variance or standard deviation, ensuring that the sample statistic is an unbiased estimator.
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 point estimator of the population mean would be the sample mean.
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.
