STATISTICAL INFERENCE PART IV CONFIDENCE INTERVALS AND HYPOTHESIS TESTING 1.
Using Inference to MAKE DECISIONS The Type I and Type II Errors in Hypothesis Testing.
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Transcript of Using Inference to MAKE DECISIONS The Type I and Type II Errors in Hypothesis Testing.
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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
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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!
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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:
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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.
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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.
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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.