Step 1

1)

The sampling distributions refers to the probability distributions of all possible values of the sample statistic for example, sample mean.

The sampling variability tells us how an estimate varies between different samples. It is often measured in terms of variance or standard deviation. There are three factors involved in variability,

The size of the population

The size of the sample

The sampling method (with or without replacement)

Step 2

2)

The central limit theorem tells us that in a random sample of size n taken from a population, its sampling distribution can be approximated to a normal distribution by taking a larger sample size. That is, whatever might be the population distribution, the sampling distribution of a sample statistic can be approximated to normal by increasing the sample size.

Step 3

3)

The confidence interval are created using the sample statistic and the margin of error.

\(CI=\overline{x}\pm Z_{\frac{\alpha}{2}}(\frac{\sigma}{\sqrt{n}}n)\)

\(=\overline{x}\pm ME\)

\(Z_{\frac{\alpha}{2}}\) represents the critical value of the normal distribution and this distribution is used if the population standard deviation is known. For unknown population standard deviation, the sample standard deviation is used with student’s t distribution.

The constructed confidence interval with say 95 or 90 percent confidence level tells us that if repeated samples were to be taken and confidence intervals were to be built, then 95 or 90 percent of these constructed confidence intervals would contain the true value of the parameter (mean).

1)

The sampling distributions refers to the probability distributions of all possible values of the sample statistic for example, sample mean.

The sampling variability tells us how an estimate varies between different samples. It is often measured in terms of variance or standard deviation. There are three factors involved in variability,

The size of the population

The size of the sample

The sampling method (with or without replacement)

Step 2

2)

The central limit theorem tells us that in a random sample of size n taken from a population, its sampling distribution can be approximated to a normal distribution by taking a larger sample size. That is, whatever might be the population distribution, the sampling distribution of a sample statistic can be approximated to normal by increasing the sample size.

Step 3

3)

The confidence interval are created using the sample statistic and the margin of error.

\(CI=\overline{x}\pm Z_{\frac{\alpha}{2}}(\frac{\sigma}{\sqrt{n}}n)\)

\(=\overline{x}\pm ME\)

\(Z_{\frac{\alpha}{2}}\) represents the critical value of the normal distribution and this distribution is used if the population standard deviation is known. For unknown population standard deviation, the sample standard deviation is used with student’s t distribution.

The constructed confidence interval with say 95 or 90 percent confidence level tells us that if repeated samples were to be taken and confidence intervals were to be built, then 95 or 90 percent of these constructed confidence intervals would contain the true value of the parameter (mean).