The ttest for paired samples

1
The t-test for paired samples

• www.ibmaths.com

2
The paired sample test can be applied to test
the difference between two small normally
distributed samples.
The samples must be identically paired.
3
As this is a significance test we need to state
the null and alternate hypotheses
Example of the paired t-test
Students sit two identical tests. One in the
morning and one in the afternoon. There results
are compared. The teacher believes that the
morning tests will score higher.
Draw a diagram to show the critical region.
Each class has 8 students and the percentages are
shown below.
1.895
Find the critical t value Tt(7). Look up p0.95
and v7.
Value 1.895
Test at the 95 significance level the claim that
the morning produces better test results.
Continued on the next page.
4
Make a table of differences between the values
Important You can get the estimate of the
variance from your GDC, but it is essential to
show your working in an exam.
Calculate your t test statistic
Compare your t test statistic with the critical
value.
Find an estimator of the population variance. For
IB you must use the formula
Conclusion Reject the null in favour of the
alternate. At the 5 level of significance there
is sufficient evidence to suggest that the
morning results are better than he afternoon
results.
This gives a value of 11.14. Square root it to
find standard deviation and verify this with your
GDC.