The Hypothesis Test About μ Determining n to control α and Power

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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

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

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

Two Restrictions on the Critical Point Z μ0 = 12 Reject H0 β α μa = 13

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

Simultaneous Solution

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