1. Two-Sample Hypothesis Test of Proportions

2. Assumptions: Two, independent SRS’s from populations
Populations at least 10n
Normal approximation for both

3. Example 1: At Community Hospital, the burn center is experimenting with a new plasma compress treatment. A random sample of 316 patients with minor burns received the plasma compress treatment. Of these patients, it was found that 259 had no visible scars after treatment. Another random sample of 419 patients with minor burns received no plasma compress treatment. For this group, it was found that 94 had no visible scars after treatment. What is the shape & standard error of the sampling distribution of the difference in the proportions of people with no visible scars between the two groups?
Since n1p1=259, n1(1-p1)=57, n2p2=94, n2(1-p2)=325 and all > 5, then the distribution of difference in proportions is approximately normal.

4. Hypothesis statements:
H0: p1 = p2
Ha: p1 > p2
Ha: p1 < p2
Ha: p1 ≠ p2
Be sure to define both p1 & p2!

5. Since we assume that the population proportions are equal in the null hypothesis, the variances are equal.
Therefore, we pool the variances!

6. Formula for Hypothesis test:
p1 = p2
So . . .
p1 – p2 =0

7. Example 4: A forest in Oregon has an infestation of spruce moths
Example 4: A forest in Oregon has an infestation of spruce moths. In an effort to control the moth, one area has been regularly sprayed from airplanes. In this area, a random sample of 495 spruce trees showed that 81 had been killed by moths. A second nearby area receives no treatment. In this area, a random sample of 518 spruce trees showed that 92 had been killed by the moth. Do these data indicate that the proportion of spruce trees killed by the moth is different for these areas?

8. Have 2 independent SRS of spruce trees
Assumptions:
Have 2 independent SRS of spruce trees
Both distributions are approximately normal since n1p1=81, n1(1-p1)=414, n2p2=92, n2(1-p2)=426 and all > 5
Population of spruce trees is at least 10,130.
H0: p1=p where p1 is the true proportion of trees killed by moths Ha: p1≠p2 in the treated area p2 is the true proportion of trees killed by moths in the untreated area
Use Technology to do a two sample Test of proportions
P-value =
a = 0.05
Since p-value > a, I fail to reject H0. There is not sufficient evidence to suggest that the proportion of spruce trees killed by the moth is different for these areas