1. The Hypothesis Test About μ Determining n to control α and Power
BM 330 Lecture Series
The Hypothesis Test About μ
Determining n to control α and Power

2. Mini-case: Medical Emergency Services
A major west coast city provides emergency medical services based on a multiple hospital system. The ambulance service goal is to respond to medical emergencies with a mean of 12 minutes or less. The director of medical services would like to formulate a hypothesis test to investigate a concern that the criterion is not being satisfied. Assume the population standard deviation is 3.2 minutes. What sample size should be used to ensure a significance level of 0.05 and a power of 0.85 when the mean response time is 13 minutes? α
β = 0.15 given μa = 13

3. The Hypotheses
H0: μ ≤ 12 minutes Ha: μ > 12 minutes

4. Two Restrictions on the Critical PointZ
μ0 = 12
Reject H0 β α
μa = 13

5. Type I error Power (Type II error) Reject H0 “Accept” H0
I. Sampling Distribution of when μ0 = 12
Type I error
α = 0.05
1.645 12 13
Reject H0
II. Sampling Distribution of when μa = 13
Power (Type II error)
β = 0.15
Power = 0.85
-1.04

6. Simultaneous Solution

7. Formulas
Formula for all one-sided tests about μ: Formula for all two-sided tests about μ: