Sampling distributions

What are the three most important properties of a sampling distribution?

1. The mean of the sampling distribution 2. The standard deviation of the sampling distribution 3. The shape of the sampling distribution

Summary about the central limit theorem:

As N gets larger, the distribution of the sample means will closely approximate a normal distribution because whenever you take a sample from a population, the sample means are then expected to be near the population mean and when you take many different samples, you expect the sample means to pile around the population mean, resulting in a normal shaped distribution.

What makes a sample size sufficiently large for the central limit theorem?

If the population itself is normally distributed, then any sample size is sufficiently large (even a sample size of 1). If the population is not normally distributed, then a sample size between 30 and 100 is needed.

What is the sampling distribution of the mean?

It gives the probability that any single random sample will have a particular mean. Or, the probability of getting a particular mean each time you select a random sample and compute its mean.

What does the standard error measure?

It measures variability in the sampling distribution, or measures exactly how much difference should be expected on average between a sample mean and a population mean. *The standard error of the mean only equals the standard deviation of the population when the sample size is 1.* Also, for any sample size 2 or more, the standard error is less than the standard deviation of the population. (As the sample size increases, standard error gets smaller)

What is the central limit theorem?

It provides a precise description of the distribution that would be obtained if you calculated the distribution of the sample mean. The theorem says that the *shape of the sampling distribution of the mean will approximate a normal curve if the sample size is sufficiently large.* However,

What is the standard deviation of the sampling distribution called?

The standard error of the mean, or the standard error.

What is meant by sampling with replacement?

When you create all the possible random samples that can be taken from a population: all possible combinations.

The mean of the sampling distribution always equals the

mean of the population Mx = M

Symbols:

µ: population mean sigma: population standard deviation (pic) Xbar: sample mean *S*: sample standard deviation