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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.
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Why you need sampling distribution?
in order to calculate the mean of the sample's mean and also to calculate the standard deviation of the sample's
How do you calculate the mean of the sampling distribution of the sample proportion?
i dont no the answer
The distribution of sample means consists of?
A set of probabilities over the sampling distribution of the mean.
Why is the normal probability distribution widely used in practice?
Suppose you have a random variable, X, with any distribution. Suppose you take a sample of n independent observations, X1, X2, ... Xn and calculate their mean. Repeat this process several times. Then as the sample size increases and the number of repeats increases, the distribution of the means tends towards a normal distribution. This is due to the Central Limit Theorem. One consequence is that many common statistical measures have an approximately normal distribution.
How do you calculate standard deviation without a normal distribution?
You calculate standard deviation the same way as always. You find the mean, and then you sum the squares of the deviations of the samples from the means, divide by N-1, and then take the square root. This has nothing to do with whether you have a normal distribution or not. This is how you calculate sample standard deviation, where the mean is determined along with the standard deviation, and the N-1 factor represents the loss of a degree of freedom in doing so. If you knew the mean a priori, you could calculate standard deviation of the sample, and only use N, instead of N-1.
The distribution of sample means is not always a normal distribution Under what circumstances will the distribution of sample means not be normal?
The distribution of sample means will not be normal if the number of samples does not reach 30.
Why you need sampling distribution?
in order to calculate the mean of the sample's mean and also to calculate the standard deviation of the sample's
What happens to the distribution of the sample means if the sample size is increased?
the means does not change
How do you calculate the mean of the sampling distribution of the sample proportion?
i dont no the answer
Does the distribution of sample means have a standard deviation that increases with the sample size?
No, it is not.
Can one treat sample means as a normal distribution?
Not necessarily. It needs to be a random sample from independent identically distributed variables. Although that requirement can be relaxed, the result will be that the sample means will diverge from the Normal distribution.
The distribution of sample means consists of?
A set of probabilities over the sampling distribution of the mean.
What is the sampling distribution of sample means and why is it useful?
Frequently it's impossible or impractical to test the entire universe of data to determine probabilities. So we test a small sub-set of the universal database and we call that the sample. Then using that sub-set of data we calculate its distribution, which is called the sample distribution. Normally we find the sample distribution has a bell shape, which we actually call the "normal distribution." When the data reflect the normal distribution of a sample, we call it the Student's t distribution to distinguish it from the normal distribution of a universe of data. The Student's t distribution is useful because with it and the small number of data we test, we can infer the probability distribution of the entire universal data set with some degree of confidence.
Is the distribution of sample means always a normal distribution If not why?
It need not be if: the number of samples is small; the elements within each sample, and the samples themselves are not selected independently.
Will the distribution of the sample means follow the uniform distribution?
The distribution of the sample means will, as the sample size increases, follow the normal distribution. This is true for any given distribution (e.g. does not need to be a normal distribution). This concept is from the central limit theorem. It is one of the most important concepts in statistics, along with the law of large numbers. An applet to help you understand this concept is located at: http:/www.stat.sc.edu/~west/javahtml/CLT.html
What does the Central Limit Theorem say about the traditional sample size that separates a large sample size from a small sample size?
The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30.
How can you compare means of two samples when the samples are chi square distributed?
According to the Central Limit Theorem if the sample size is large enough then the means will tend towards a normal distribution regardless of the distribution of the actual sample.
