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The parent probability distribution from which the statistic was calculated is referred to as f(x) and cumulative distribution function as F(x). The sampling distribution and cumulative distribution of a statistic is commonly referred to as g(y) and G(y) where Y is the random variable representing the statistic. There are numerous other notations.

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2010-04-02 13:53:47
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Q: What is sampling distribution of a statistic called?
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True or False A sampling distribution is a probability distribution for a statistic?

The statement is true that a sampling distribution is a probability distribution for a statistic.

What is a sampling distribution?

The sampling distribution for a statistic is the distribution of the statistic across all possible samples of that specific size which can be drawn from the population.

What do you mean by a statistic and its sampling distribution?

A statistic is a summary measure of some characteristic of a population. If you were to take repeated samples from the population you would not get the same statistic each time - it would vary. And the set of values you would get is its sampling distribution.

How does sampling distribution work in statistics?

Sampling distribution in statistics works by providing the probability distribution of a statistic based on a random sample. An example of this is figuring out the probability of running out of water on a camping trip.

What is Confidence Intervals of Standard Error?

The standard deviation associated with a statistic and its sampling distribution.

What is the purpose of a sampling distribution?

A statistic based on a sample is an estimate of some population characteristic. However, samples will differ and so the statistic - which is based on the sample - will take different values. The sampling distribution gives an indication of ho accurate the sample statistic is to its population counterpart.

What is the distribution of values taken by a statistic in all possible samples of equal size from the same population?

It is the sampling distribution of that variable.

What is the mean of the sampling distribution equal to?

The mean of the sampling distribution is the population mean.

What distribution is a sampling distribution referring to?

A sampling distribution refers to the distribution from which data relating to a population follows. Information about the sampling distribution plus other information about the population can be inferred by appropriate analysis of samples taken from a distribution.

What is the meaning of Sampling distribution of the test statistic?

Given any sample size there are many samples of that size that can be drawn from the population. In the population is N and the sample size in n, then there are NCn, but remember that the population can be infinite. A test statistic is a value that is calculated from only the observations in a sample (no unknown parameters are estimated). The value of the test statistic will change from sample to sample. The sampling distribution of a test statistic is the probability distribution function for all the values that the test statistic can take across all possible samples.

How do you find the confidence intervals?

See: Includes a worked out example for the confidence interval of the mean of a distribution. In general, confidence intervals are calculated from the sampling distribution of a statistic. If "n" independent random variables are summed (as in the calculation of a mean), then their sampling distribution will be the t distribution with n-1 degrees of freedom.

What is the difference between a probability distribution and sampling distribution?

A sampling distribution function is a probability distribution function. Wikipedia gives this definition: In statistics, a sampling distribution is the probability distribution, under repeated sampling of the population, of a given statistic (a numerical quantity calculated from the data values in a sample). I would add that the sampling distribution is the theoretical pdf that would ultimately result under infinite repeated sampling. A sample is a limited set of values drawn from a population. Suppose I take 5 numbers from a population whose values are described by a pdf, and calculate their average (mean value). Now if I did this many times (let's say a million times, close enough to infinity) , I would have a relative frequency plot of the mean value which will be very close to the theoretical sampling pdf.

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