9_6_11_hypo_testing1 - Errors in hypothesis testing Ho is...

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CE4001 Transportation Safety 1 Errors in hypothesis testing Ho is true Ho is false Reject Ho Type I error = Correct decision Do not reject Ho Correct decision Type II error = Type I = false positive Type II = false negative; cannot generally be computed because it depends on the population mean but can be estimated for given values of μ, σ 2 and n. Give some examples of Type I and II errors.
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CE4001 Transportation Safety 2 Errors in hypothesis testing Ho is true Ho is false Reject Ho Type I error = Correct decision Do not reject Ho Correct decision Type II error = Example: Determining if crashes are due to the new signal heads Type I (false positive), Ho is true so no real change, but still ascribe the change to the treatment e.g. reduction in crashes due to random fluctuation but ascribed to the new signal installation Type II (false negative), Ho is false so there was real change, but did not identify the treatment as effective e.g. reduction due to signal installation but not identified as such
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CE4001 Transportation Safety 3 Why is it important to note both types of errors?
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CE4001 Transportation Safety 4 Why is it important to note both types of errors? One could artificially emphasize one error to the detriment of the other. Give an example.
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CE4001 Transportation Safety 5 Why is it important to note both types of errors? One could artificially emphasize one error to the detriment of the other. e.g. red-light running cameras that flag 100% of all vehicles, so 0 Type II error. It will never miss a speeder, but will issue innocent tickets. (i.e. an unacceptable number of false positives)
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CE4001 Transportation Safety 6 Type I & II Errors Want to minimize and . Usually, is specified as the significance level, i.e. confidence level = 1- . e.g. 1% significance level = 99% confidence
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CE4001 Transportation Safety 7 Type I or II Misclassification?
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CE4001 Transportation Safety 8 t-test n s x t Test statistic for when 2 is unknown. Distribution is similar to the normal distribution except Z distribution assumes 2 is known.
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CE4001 Transportation Safety 9 t table with right tail probabilities df = degrees of freedom, or n-1 (n is number of samples)
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CE4001 Transportation Safety 10 df\p 0.400 0.250 0.100 0.050 0.025 0.010
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9_6_11_hypo_testing1 - Errors in hypothesis testing Ho is...

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