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Using Inference to MAKE DECISIONS

Learn about Type I and Type II errors in hypothesis testing and how to make decisions based on statistical inferences. Explore the concept of power, significance levels, sample sizes, and error probabilities. Discover the importance of P-values and maximizing power in statistical analysis.

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Using Inference to MAKE DECISIONS

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  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.

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