t-test for One Sample

Here's an example:

The average sleep time is supposed to be 8 hours a day (m).
We think college students sleep a different amount, maybe more - maybe less.
We survey ten students to see how much they sleep.
The data are as follows (each cell represents a student):

6	5	4	3	7
5	5	5	6	6

Here's the output from a computer package.

One-Sample Statistics
	N	Mean Std.	Deviation Std.	Error Mean
SLEEP	10	5.2000	1.1353	.3590

One-Sample Test Test Value = 8
	t	df	Sig. (2-tailed)	Mean Difference
SLEEP	-7.799	9	<.001	-2.8000

Take away points:

Sample mean is 5.2

It is compared against 8.

The difference is -2.8 hours

The difference is significant as the t -value is so big and the probability of this being chance is so low.

Here's another example:

8	7	7	8	7
8	9	7	7	6.5

Here's the output from a computer package.

One-Sample Statistics
	N	Mean Std.	Deviation Std.	Error Mean
SLEEP	10	7.5000	.8165	.2582

One-Sample Test Test Value = 8
	t	df	Sig. (2-tailed)	Mean Difference
SLEEP	-1.936	9	.085	.5000

Try to figure out why this data set is not significant. I've highlighted the crucial points.

Bottom Line:

You get the data.
You calculate the mean and standard deviation.
You calculate the t ratio.
You look it up.
If the probability of t is less than .05 or .01, you have significance.
You conclude the group is different from the Null Hypothesis mean.

Remember this:

Big t
Small p
Small p - Significance