1. Significance Tests and Two Proportions
Presentation 9.5

2. Working with Two Proportions
Be sure to define your proportions so you can keep track of them.
For example:
1: males
2: females
Use proper notation:
Sample size
Population proportion
Sample proportion
Population 1 n1 p1
Population 2 n2 p2

3. Properties: Sampling Distribution of p1- p2
If the two random samples are independent, the following properties hold:
If both n1 and n2 are large [n1 p1  10, n1(1- p1)  10, n2p2  10, n2(1- p2)  10], then p1 and p2 each have a sampling distribution that is approximately normal

4. Setting up the Two Proportion Test
Check the conditions
Independent samples
Large enough samples
n1p110, n1(1- p1)10, n2p210, n2(1- p2)10
Write Hypotheses
Null Hypothesis (the two proportions are equal)
Ho: p1=p2 or Ho: p1-p2=0
Alternate Hypothesis
Ha: p1<p2 or Ha: p1-p2<0
Ha: p1>p2 or Ha: p1-p2>0
Ha: p1≠p2 or Ha: p1-p2 ≠ 0

5. Conducting the Two Proportion Test
Calculations
Test Statistic z
We will use the calculator for these calculations
p-value
Calculate this as you always have using normalcdf

6. Example #1: Big Brother
A survey of 356 workers showed that 192 of them said that it was unethical for the company to monitor employee . When 106 senior-level bosses were surveyed, 38 said that it was seriously unethical for the company to monitor employee . Is there a significant difference between the workers’ opinion and the bosses’ opinion of monitored ?

7. Count (# opposed to monitoring)
Example #1: Big Brother
First, check conditions.
These check out fine as the sample sizes are rather large
Set up hypotheses.
Ho: p1=p2
Ha: p1≠p2
Sample size
Count (# opposed to monitoring)
Sample proportion
p-hat
Population 1:
Workers
356
192
0.5393
Population 2:
Bosses
106 38
0.3585

8. Example #1: Big Brother
Conduct calculations by using the 2-proportion z test
Enter in your statistics
Record your test statistic and p-value (which can also be obtained using 2normalcdf(3.2687,99)

9. Example #1: Big Brother Conclusions
With such a small p-value, we reject the null
There is sufficient evidence to suggest that there is a difference between the proportion of workers who are opposed to monitoring and the proportion of bosses who are opposed to monitoring.

10. Example #2: Well Water
A major court case on the health effects of drinking contaminated water took place in the town of Woburn, Massachusetts. A town well was contaminated with industrial chemicals. During the period when the well was open, 16 birth defects out of 414 births. When this particular well was shut off from and water was supplied from other wells, 3 out of 228 birth defects were reported. The plaintiffs suing the firm responsible for contaminating the well claim that the rate of birth defects is higher when the contaminated well was in use. Conduct a significance test to determine if the plaintiffs have a case.

11. Example #2: Well Water
Conduct this test on your own. Following are the results:
Test Statistic: z =
p-value:
At the 5% level, reject the null
At the 1% level, fail to reject the null
If you have questions about these answers, post them in the discussion board!

12. Significance Tests and Two Proportions
This concludes this presentation.