1. Significance Test for the Difference of Two Proportions
Section 8.4
Significance Test for the Difference of Two Proportions

2. Quiz 8.3 – 8.4 tomorrow
1 side of a note card

3. Suppose:
We have two populations.

4. Suppose:
We have two populations.
The proportion of successes for each population is 0.2 so …

5. Suppose:
We have two populations
The proportion of successes for each population is 0.2 so p1 = p2

6. Suppose:
We take a pair of samples of size 30 from each population and calculate the difference in their proportions,

7. Suppose:
We take a pair of samples of size 30 from each population and calculate the difference in their proportions,
We repeat this process 5000 times

8. Next, we do this same process for samples of size 50 and 100
Suppose:
We take a pair of samples of size 30 from each population and calculate the difference in their proportions,
We repeat this process 5000 times
Next, we do this same process for samples of size 50 and 100

9. Next, we do this same process for samples of size 50 and 100
Suppose:
We take a pair of samples of size 30 from each population and calculate the difference in their proportions,
We repeat this process 5000 times
Next, we do this same process for samples of size 50 and 100
Where do we expect the center of the distribution to be?

10. Where do we expect the center of the distribution to be?
0 because p1 = p2
Recall, the mean of the differences is equal to the difference of the means.

12. As n1 and n2 increase?
Shape:
Center:
Spread:

13. As n1 and n2 increase?
Shape: more normal
Center:
Spread:

14. As n1 and n2 increase?
Shape: more normal
Center: stays at 0
Spread:

15. As n1 and n2 increase? Shape: more normal Center: stays at 0
Spread: decreases

16. Standard Error As n1 and n2 increase, the standard error decreases.
To find standard error, use formula:
SE =

17. Standard Error

18. Page 536, P48

19. Page 536, P48
(a) After millions of repetitions, we would expect and to both equal 0.12.
Thus, the expected value of the difference of
would be = 0.

20. Page 536, P48

21. Page 536, P48

22. Page 536, P48 d. Using the calculator, normalcdf(.05,1E99, 0, .0154)
gives approximately
Note: This is not a standard normal distribution so must also use mean and standard error.

23. Time to go to work
on Fathom Lab 8.4a!
Due: Wednesday

24. Questions?