# Suppose you compile all possible samples of 25 children of preschool age in your school district. If you calculate the mean of each sample (M) and create a frequency distribution of these means, this distribution is referred to as the

Question

Suppose you compile all possible samples of 25 children of preschool age in your school district. If you calculate the mean of each sample (M) and create a frequency distribution of these means, this distribution is referred to as the

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Step 1

Sampling distribution of sample mean:

A sampling distribution of the sample mean for a given sample of size n consist collection of the means of the all possible samples of size n from the population. If the parent population is a normal distribution, then the sampling distribution of the sample mean will also follow normal distribution.

Step 2

Points on sampling distribution of the sample mean:

• If the true population distribution of a random variable, say, x, is normal with parameters, mean μ and standard deviation σ, then, whatever be the size (n) of the sample taken from the population, the distribution of the sample mean is also normal, with parameters, mean μ and standard deviation σ/√n.
• Even if the true population distribution of a random variable, say, x, is not normal and has population mean μ, standard deviation σ, then, for a large size (n ≥ 30) of a sample taken from the population, the distribution of the sample mean is approximat...

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