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Would one expect more variance with a larger sample size in a chi distribution?
Wiki User
∙ 14y ago
The larger your sample size, the less variance there will be.
For instance, your information is going to be much more substantial if you took 1000 samples over 10 samples.
Wiki User
∙ 14y ago
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How do you calculate distribution of sample means?
The sample mean is distributed with the same mean as the popualtion mean. If the popolation variance is s2 then the sample mean has a variance is s2/n. As n increases, the distribution of the sample mean gets closer to a Gaussian - ie Normal - distribution. This is the basis of the Central Limit Theorem which is important for hypothesis testing.
What would happen to the sampling distribution of the mean if you increased the sample size from 5 to 25?
The variance of the estimate for the mean would be reduced.
Can the variance of a sample be larger than the sample mean?
Yes, Mean is given by, E(X) sum of samples / no. of samples. Variance is Var.(X) = E(X^2) - [E(X)]^2. It is the 1st term which makes the variation of variance independent of mean. In other words, Variance gives a measure of how far the samples are spread out.
What is the sample variance of 5781010 and 14?
The variance is: 1.6709957376e+13
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.
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.
How does the number of repetitions effect the shape of the normal distribution?
When we discuss a sample drawn from a population, the larger the sample, or the large the number of repetitions of the event, the more certain we are of the mean value. So, when the normal distribution is considered the sampling distribution of the mean, then more repetitions lead to smaller values of the variance of the distribution.
How do you calculate distribution of sample means?
The sample mean is distributed with the same mean as the popualtion mean. If the popolation variance is s2 then the sample mean has a variance is s2/n. As n increases, the distribution of the sample mean gets closer to a Gaussian - ie Normal - distribution. This is the basis of the Central Limit Theorem which is important for hypothesis testing.
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.
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.
What would happen to the sampling distribution of the mean if you increased the sample size from 5 to 25?
The variance of the estimate for the mean would be reduced.
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 a difference between F statistics F distribution?
An F-statistic is a measure that is calculated from a sample. It is a ratio of two lots of sums of squares of Normal variates. The sampling distribution of this ratio follows the F distribution. The F-statistic is used to test whether the variances of two samples, or a sample and population, are the same. It is also used in the analysis of variance (ANOVA) to determine what proportion of the variance can be "explained" by regression.
Can the variance of a sample be larger than the sample mean?
Yes, Mean is given by, E(X) sum of samples / no. of samples. Variance is Var.(X) = E(X^2) - [E(X)]^2. It is the 1st term which makes the variation of variance independent of mean. In other words, Variance gives a measure of how far the samples are spread out.
Does use of chi-square demand a random sample?
Well, sort of. The Chi-square distribution is the sampling distribution of the variance. It is derived based on a random sample. A perfect random sample is where any value in the sample has any relationship to any other value. I would say that if the Chi-square distribution is used, then every effort should be made to make the sample as random as possible. I would also say that if the Chi-square distribution is used and the sample is clearly not a random sample, then improper conclusions may be reached.
Is sample variance unbiased estimator of population variance?
No, it is biased.
What is the sample variance of 5781010 and 14?
The variance is: 1.6709957376e+13
