Instructor: Hello, students.
Welcome to example five, chapter seven.
In this example, we will learn how to perform
hypothesis testing for two sample
independent dichotomous outcome data.
For this problem we will use problem 27 from our textbook.
And the problem states, use the data shown in problem 25
and test if there is a significant difference
in the proportion of diabetic participants
in the placebo group
as compared to the standard drug group.
Use a 5% level of significance.
Now for your convenience, I have copied and pasted
the table here and before we move forward to step one,
I just want to clarify
the two samples here are independent
because we are comparing the placebo group
to the standard drug group.
And because we are evaluating proportion,
the data here is dichotomous
and given the sample size here, we will be using Z test.
Now in step one, we are stating our hypotheses
and we are also determining the level of significance.
The null hypothesis here states that the proportion
of diabetic participants is equal
and the alternative hypothesis states that it is not equal.
In step two, we will be selecting
the appropriate test statistics
and for step three we will be setting up our decision rule
and we will reject the null hypothesis
if our Z calculated is less than or equal to 1.960,
or if our Z calculated is greater than
or equal to 1.960.
Now we will be computing the test statistics.
Now here we will need to calculate
the overall proportion p-hat
and that will be x1 + x2 divided by n1 + n2.
So we get those figures
and we perform the calculation
and our p-hat is 0.3.
Now, when we substitute the values
and we compute our test statistics,
we see that our Z here is 0.49.
Of course, the values here for p1-hat and p2-hat
are provided to us in the table,
and the p-hat is the one we just calculated
and the n1 and the n2 are also provided to us.
So again, once we insert these values into the formula
and we perform the algebra,
we find out that our Z calculated is equal to 0.49.
Now as far as our conclusion is concerned,
here, we will fail to reject the null
because 0.49 is not less than
or equal to negative 1.960
and 0.49 is not greater than or equal to positive 1.960.
Therefore, we do not have statistically significant evidence
at alpha at 0.05 to show
that there is a difference in the proportion
of diabetic participants in the placebo group
as compared to the standard drug group.
Thank you for your time and attention
and I'll see you in the next video.