Instructor: Dear students, this is our first example
for chapter six.
In this example, we are going to learn
how to calculate confidence interval
for a small sample size of eight
using t-distribution.
Now, the problem here is from our textbook, problem 15.
The problem states, a pilot study is run to investigate
the feasibility of recruiting pregnant women
into a study of risk factors for pre-term delivery.
Women are invited to participate
at their first clinical visit for prenatal care.
The following represent the gestational ages in weeks
of women who consented to participate in the study.
Compute a 95% confidence interval
for the mean gestational age
of women enrolling in the study.
So here,
the numbers or values are given,
and the first step is for us to calculate the mean
and the standard deviation.
Now, here, I have used the short formula
to calculate the standard deviation,
because the objective here is not to calculate
the standard deviation or the mean,
but rather, to learn how to calculate
the confidence interval.
Now, I also want to let you know that
for this biostatistics
ER problem, the solution here is typed
because once I heard from a student
that all of my biostat ER examples are solved by hand.
Hence, I have used this typed solution here,
but I am going to go through this step by step.
So the next thing we have to see here is
the degrees of freedom,
because based on that, we have to obtain
our t-value from the back of our book.
So our degrees of freedom here is going to be n - 1.
And what is our n?
Our n is eight.
So when we take eight and deduct one, we get seven.
So based on 95% confidence interval
and degrees of freedom of seven,
we get the t-value again from the back of our book,
which is 2.365.
Now, once we have all the
values at our
hand, this is basically plugging it into the formula.
And the formula here is X bar +/- t,
which is the t we just obtained, the t-value.
S divided by square root of n.
So our X bar here is 14.8.
The t-value here is 2.365.
The standard deviation we calculated previously,
which is five, and the sample size, n, is eight,
so it is the square root of eight.
So, when we perform the algebra,
we get 14.8
+/- 4.18.
And when, again, we solve that,
what we get is 10.6 and 19.0.
So that is basically our 95% confidence interval
for the mean gestational age
of women enrolling in the study.