Instructor: Hello students,
Again, this is example 3 for our chapter 6.
The example I'm using here is from our book.
It is Problem 22.
The problem here states,
"The incubation period, the time between exposure
and development of symptoms,
has been reported to be different
in older and younger individuals.
One such study compared individuals under 65 years of age
to those 65 years and older and found the following."
So here's the table where the data is reported,
and we have the mean and standard deviation
as per incubation period days also given to us.
And now the question is asking us,
"Compute a 95% confidence interval
and estimate for the difference in mean incubation periods
between younger and older adults.
Is there a statistically significant difference
in mean incubation periods?
Justify your response."
So again, this is an example when I am going to use
the typed response
instead of working the problem by hand.
So the first thing we have to do is select
the correct formula, which is given here.
And once we have selected the correct formula,
we need to look at how we are going to calculate the Sp.
So for the Sp here, I have already,
again, given you the formula
as well as I've shown you the calculation.
But keep in mind, before the Sp,
we needed to look at the ratio of the sample variance
and I calculated there
and I found the sample variance to be 0.61.
So therefore we are calculating the Sp here
given the formula and our Sp here is 0.93.
So here now we are going to insert the values
that were given to us.
So x bar 1 minus x bar 2.
So x bar 1 here is 7.5
and x bar 2 is 11.1.
Then of course we have to obtain the z value, 95%,
which we already have looked up from table 1B
and it is 1.96.
Then the Sp that we just calculated is 0.93.
And then here we have to insert the numbers,
our sample size basically, n1 and n2.
So our n1 is 55 and our n2 is 45.
So when we basically solve this equation algebraically,
we get the value negative 3.6 plus minus 0.37.
And then when we solve that further,
we get minus 4.0 to minus 3.2.
So what does that mean?
That means that we are 95% confident
that the difference in true mean incubation
is anywhere between 3.2 to 4.0 days longer
in older patients as compared to younger patients.