Inference for

1

• Lesson 28
• Inference for
• Two Proportions

2
Take samples of sizes n1 and n2,
in which we observe X1 and X2 successes
3
If n1 and n2 are large, then
An approximate 100(1-a) C. I. for (p1 p2) is




4
To test H0 p1 p2 0 (i.e. H0 p1 p2
) against some alternative, first calculate
Substitute this for both p1 and p2 in the
standard error
5
The test statistic is then
Again, use the usual Z-test rejection regions
6
n1 100
X1 12 w/ Lung Ca
Smokers
Non-smokers
n2 150
X2 3 w/ Lung Ca
95 C. I. for (p1 - p2)
? (1.96)
(.12 - .02)
? (.032 , .168)
7
H0 p1 p2
Reject H0 if Z0 gt Z.95 1.645
H1 p1 gt p2
.06
- .02
.12
3.26
Reject H0
Higher proportion of lung cancer among smokers
8
n1 18
X1 11 w/ sneakers
Female
Male
n2 32
X2 28 w/ sneakers
H0 p1 p2
H1 p1 lt p2
Reject H0 if Z0 lt -Z.90 -1.282
9
.78
- .875
-2.16
Reject H0
Lower proportion of wearing sneakers among
females than among males
10
95 C. I. for (p1 - p2)
? (1.96)
? (-.517 , -.011)