Hypothesis Testing The z-test for Proportions

2. Collect the data
3. Compute the test statistic
z =
4. Make the Decision
• Accept H0 if: − z ≤ z ≤ z
• Reject H 0 if:
x − μ0 x − μ
n ≈ n
σ s
α / 2
α / 2
z < −z
z > z
0
α / 2 or
The one tailed test
α / 2
To test
H0 : μ ≤ μ0
(some specified value of μ)
against
HA : μ > μ0
1. Use the test statistic
z =
x − μ0 x − μ
n ≈ n
σ s
2. Use as the Acceptance and Critical Region
• Accept H0 if: z ≤ zα
/ 2
• Reject H0 if: z > z
Accept H 0
0
α / 2
zα
0
α
Reject H 0
z
The one tailed test – other direction
To test
H0 : (some specified value of μ)
against
HA : 0 μ
μ ≥ μ0
μ <
Acceptance and Critical Region
• Accept H 0 if:
• Reject H 0 if:
Test Statistic
α
Reject H 0
z =
z ≥ −z
z < −z
α / 2
α / 2
x − μ0 x − μ
n ≈ n
σ s
Expect z to be negative if H 0 is false
Example:
The Acceptance and Critical region:
− zα
Accept H 0
We are interested in measuring the concentration of
lead in water and we want to know if it exceeds the
threshold level μ 0 = 10.0
We take n = 40 one-litre samples measuring the
concentration of lead.
Statistical results:
x
= 12 . 1 and s = 1.
2
0
0
z
8