What is a sampling distribution? If we are considering the sample mean, how do we calculate...

What is a sampling distribution?

If we are considering the sample mean, how do we calculate the standard error of the sample mean?

If we are considering the sample proportion, how do we calculate the standard error of the sample proportion?

Expert Solution

The sampling distribution is nothing but the probability distribution of the sample. It is not possible in any research to take data from every individual in the world. So a finite group of investigation samples is taken and research is carried out on them.

For example- In the estimation of population mean, we say that sample mean is normally distributed, here we say sample mean and not population mean. It means that the sampling distribution of the mean is normal.

Now for the next two parts:

The standard error is just the standard deviation of data.

For sample mean, the standard deviation is calculated by the formula

For sample proportion, let p be sample proportion, the standard deviation is calculated by

Again these are just standard deviations of samples, which on working out in proof according to known statistic comes out to be these.

orchestra answered 1 year ago

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