Using Inference to Using Inference to MAKE DECISIONS MAKE DECISIONS The Type I and Type II Errors in The Type I and Type II Errors in Hypothesis TestingHypothesis Testing

Power and type I and II errors

ℳ=6.7x=6.48z=-2.20

P=0.0139

There is about 1.4% chance that the city manager would obtain a sample of 400 calls with a mean

response of 6.48 minutes or less. The small P-value provides strong evidence against Ho and in favor the

Ha where <6.7ℳ

Ho: = 6.7 minutesℳHa: < 6.7 minutesℳ

z= x-ℳσ/√n

z= 6.48-6.72/√400

z= -2.20

Paramedics!

POWER CALCULATIONPOWER CALCULATION• Increase α. A test at the 5% significance level will

have a greater chance of rejecting the alternative than a 1% test because the strength of evidence required for rejection is less.

• Consider a particular alternative that is farther away from μ0. Increase the sample size, so we will have a better chance of distinguishing values of μ.

• Decrease σ. This has the same effect as increasing the sample size:

The power of a significance test measures its ability to detect an alternative hypothesis. The power against a specific alternative is the probability that the test will reject H0 when the alternative is true.

BEST ADVICE IN BEST ADVICE IN MAXIMIZING POWERMAXIMIZING POWER

choose as high an αlpha level (Type I error probability) as you are willing to risk and as large a sample size as you can afford.

What you should have What you should have learned?learned?

A P-value is the probability that the test would produce a result at least as extreme as the observed result if the null hypothesis really were true. Very surprising outcomes (small P-values) are good evidence that the null hypothesis is not true.