Estimating a population parameter entails a confident centerfold,

which is always of the form point estimate plus or minus a margin of error.

The margin of error is a critical value times the standard error, and since we're

doing inference on the mean, we're going to use the t star for our critical value.

This standard error of x bar is s over the square root of n, so

the only new item here is the critical t score.

To figure out this value, we need to determine the degrees of

freedom associated with the t distribution that we need to use for this data.

When working with data from only one sample,

an estimating a single mean, the degrees of freedom is n-1.

We lose one degree of freedom because we're estimating the standard error

of the sample mean using the sample standard deviation.

Putting all of this together, the confidence interval for

a single population mean can be estimated using x bar plus or

minus t star with n minus 1 degrees of freedom times s over the square root of n.

There are variety of ways of finding the critical t score.

The first is using the t table.

First calculate the degrees of freedom which in this case is 22- 1, 21.

Then locate that row on the t table and find the corresponding tail area for

the desired confidence level.

At this point it's a good idea to draw the normal curve and

mark the confidence level in the center of the curve.

If we have 95% in the center, then we have 5% left for the two tails.

We locate this value as the two tail area on the table and grab the critical

t score at the intersection of the row and the column we marked, which is 2.08.

Alternatively, we can find the critical t score using R.

Once again, let's draw the normal curve and

mark our confidence level in the center of the curve.