Using Inference to MAKE DECISIONS

1. Using Inference to MAKE DECISIONS • The Type I and Type II Errors in Hypothesis Testing

2. z= x-ℳ z= 6.48-6.7 Ho: ℳ = 6.7 minutes Ha: ℳ < 6.7 minutes z= -2.20 2/√400 σ/√n ℳ=6.7 x=6.48 z=-2.20 P=0.0139 Power and type I and II errors Paramedics! 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 ℳ<6.7

3. POWER 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:

4. 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.

5. BEST ADVICE IN MAXIMIZING 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.

6. What you should have 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.