Instructor: Hello students, and welcome
to Biostat ER Chapter 8: Example 2.
In this example, we will learn how to calculate sample size
for one sample continuous outcome
to determine confidence interval,
and we will utilize the data from example one.
The problem statement hence is going to be the same,
but I will read it again.
The issue here is that we have collected some data,
and we need to know if our sample mean is different
from some established mean, which is 100.
We want a hypothesis test with 80% power,
and we know that we will fail
to reject the null hypothesis
within a margin of error of five.
Therefore, if our mean is between 95
and 105, we know that we will fail
to reject the null hypothesis.
From publications for similar studies,
we know that the standard deviation is between 8.5 and 9.5.
So the question is how many subjects are required
to determine a confidence interval that will have a margin
of error no greater than five?
So again, for your convenience,
I have summarized the information here,
as you can take a look at it very quickly.
And I want to also emphasize
that the Z value here is again going to be 1.96.
I've also inserted the formula here,
and it is N equal to Z times sigma divided
by E and the whole square.
Now the standard deviation,
which was obtained from previous literature is a range,
and we want to use the highest value
as it'll give us the most variation
and ensure that we have enough subjects in the study.
We are here erroring on the side of caution,
and we want to ensure that we are enrolling enough people.
So once we insert all the values, so here Z is going
to be 1.96, sigma is going to be 9.5,
the E is going to be five.
So we insert all the values and we perform the algebra,
we get 13.9.
And as always, we are going to round it up
and that's going to be 14.
So 14 subjects here are required.