Instructor: Dear students,
in this example we are going to learn
how to create a confidence interval
for matched samples of continuous data.
We have matched data
when we have matched case-control studies, sibling studies.
Twin studies are data taken on the same individuals
at different points in time.
So for this example, which is a hypothetical example,
we are going to run an experiment.
We recruit a random sample of 10 individuals
and ask them how many times a week they exercise.
Based on the responses,
we realize that most of the individuals, if not all,
might benefit from enrolling into an exercise program.
Hence, we ask them if they're interested to enroll,
and they all agree.
Six months later, we ask them the same question
and collect the data again.
The fictitious data is shown below.
Now, as you have probably realized,
this is an example of matched sample of continuous data,
because these are the same individuals.
In contrast to
the independent samples,
the confidence interval for matched samples
is for the mean difference
as opposed to for the difference in means.
So here first, we have to write the formula,
and I'm going to write it for you here,
because we are looking for the 90% confidence interval.
This will be our formula.
We will use the t distribution here
because our sample size is below 30, it is 10,
and now we know our degrees of freedom is going to be nine.
And from the back of our book,
we get our t critical value,
which is going to be
1.833.
Now what we are going to do is plug all these numbers
into our formula.
So we are going to now do the algebra,
and what we find here is...
Of course, after doing all the algebra
and rounding up our numbers,
this is our confidence interval.
Now, one thing I want you to
understand here is
that our confidence interval here does not include a zero.
Therefore, we can state with 90% confidence
that the mean difference here has changed significantly
before after, or after the individuals enrolled into the
exercise program.
I hope this helps and I will see you in the next video.