1. Hypothesis Testing Elements of a Hypothesis Test:
Null Hypothesis H0: µ = 21 yr
2) Alternative Hypothesis HA: µ ≠ 21 yr
3) Test Statistic X
4) Decision Rule – Rejection Region R: X > 22 yr
X < 20 yr

2. Hypothesis Test as a Decision Table:
Null Hypothesis
True False
Accept H0
Reject H0
α = P(Type I Error) = P(Reject H0|H0 is True)
β = P(Type II Error) = P(Accept H0|H0 is False)

3. Analogy with US Criminal Legal System
Person
Not Guilty Guilty
Acquit
Convict

4. Use alpha to Determine the two Critical Values
α/2
α/2
µ = 21
Reject H Accept H Reject H0
Standard Normal Curve

5. Hypothesis Test:
H0: µ =21
HA: µ ≠ 21
R: X > 21.98
X < 20.02
We could also base the test upon the Standard Normal Curve:
H0: µ = 21
HA: µ ≠ 21
α = .05
R: Z > 1.96
Z < -1.96

6. Average Student Credit Load
n = X = 14.2
s = 2
H0: µ = 15 cr
HA: µ ≠ 15 cr
α = . 10
R: Z >
Z <
P-Value for a Test - Probability that H0 is True
If P-Value < α, then Reject H0
If P-Value ≥ α, then Accept H0

7. Upper Tail Test:
H0: µ ≤ µ0
HA: µ > µ0
R: Z > Zα
Coffee shop currently sells 320 cups/day
n =40 X = 330 cups/day
s = 40 cups/day
H0: µ ≤ 320 cups/day
HA: µ > 320 cups/day
α = .05
R: Z >

8. Lower Tail Test:
H0: µ ≥ µ0
HA: µ < µ0
R: Z < -Zα
Employee Absenteeism currently 10.2 day/yr
n = X = 9.3 day/yr
s = 4 day/yr
H0: µ ≥ 10.2 day/yr
HA: µ < 10.2 day/yr
α = .10
R: Z <

9. Small Sample Tests – ( n < 30 )
H0: µ = µ0
HA: µ ≠ µ0
R: t > tα/2,df=n-1
t < -tα/2,df=n-1
Hour Glass Factory:
n = X = 61 min
s = 2 min
H0: µ = 60 min
HA: µ ≠ 60 min
α = .05
R: t >
t <

10. n = X = 11 hr/wk
s = 3 hr/wk
Work-Study Hours:
H0: µ = 10 hr/wk
HA: µ > 10 hr/wk
α = .05
R: t >
20 lb Bags of Dog Food
n = X = 19 lb
s = 2 lb
H0: µ = 20 lb
HA: µ < 20 lb
α = .05
R: t <

11. Tests on the Population Proportion:
H0: p = p0
HA: p ≠ p0
R: Z > Zα/2
Z < -Zα/2
A Fair Coin?
n = X = 83
H0: p = .50
HA: p ≠ .50
α = .05
R: Z >
Z <

12. Type II Error – β = P(Accept H0|H0 is False)
Reject H0
Accept H0
Suppose µ = 22
Suppose µ = 23

13. 1 – β = Power of the Test
α = Significance of the Test
µ P(Accept H0) P(Reject H0) 21
.95
.05
21.5
.8315
.1685 22
.4840
.5160
22.5
.1492
.8508 23
.0207
.9793