Margin of Error

Margin of Error (E) is the error that can be tolerated when estimating a value.

For confidence intervals, it is calculated as the critical value multiplied by the standard error -

E = Crit Val * Std Err

First, you look up the critical value from the probability table (t or z), then you calculate the standard error. Multiply these together.

Margin of Error tells you how much 'cushion' to place on your estimated value.

This cushion will be larger or smaller depending on the critical value that the researcher has chosen.

However, to determine sample size (n), the margin of error is chosen, not calculated.

For example, a buyer wants to know the sample size needed to estimate the average cost of shoes. He needs the estimate to be within ten dollars of the true population mean.

In this case, you will use E=10 in the formula for solving sample size.

Degrees of Freedom

Degrees of freedom (df) equals the sample size minus the number of estimated parameters. Commonly there is only one estimator - the sample standard deviation.

df=n-k, where k is the # of parameters being estimated.

df=n-1, k = 1 for a single population using an estimated standard deviation

t-table

The t-table is used when the population standard deviation ("sigma") is unknown. Sigma is estimated using the sample standard deviation ("s"). The graph is bell-shaped.

It is related to the z-table, but with greater dispersion. Each sample size has a unique set of t-values, determined by the "degrees of freedom (d.f.)"