STATISTICS CONTINUED

The standard error of the mean

This statistic gives us an idea of how good our sample is. The narrower the limits are the closer the mean of the sample represents the mean of the population.

In other words, we are 95% sure that the mean of the population lies somewhere between:

NB We would only use this formula for n>30.  If  n<30 and we are fairly sure the population we are sampling from has normal distribution we replace 1.96 by the 95% point from our t-test tables with n-1 degrees of freedom.

·         To calculate the 95% confidence limits on your calculator

Press

Use the cursor to move to the TESTS menu

Press

This selects TInterval

You will probably find the data has already been entered for List: as L1  but if you want to use another column of data change the Lists by pressing then  and scrolling down to the list of data that you want.

Freq:1 can be left alone

C-Level: .95 sets the confidence limits at 95%

Scroll down further to select Calculate

Press

You will get the result for the 95% confidence limits for your data

Example:

TInterval
(20.926, 23.274)	(the 95% confidence limits)
= 22.1	(the sample mean)
Sx = 3.144	(the sample standard deviation)
n=30	(the sample size)

Comparing the means of two samples

Are the means from two different samples significantly different from one another?
This can be estimated by finding the standard error of the differences between the two means and comparing this with probability levels that have already been calculated. We can use this test when the size of both samples are greater than 30.

1.      First set up your "null hypothesis". This is the hypothesis that states there is no difference between the two populations.
2.  Calculate your test statistic using

Table of probability values:

• Continued
• Previous Page
• Index Page
• Top of Page

© Paul Billiet 2009