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Project 5: Evaluating Hypotheses

Intro ] [ 5.1 ] [ 5.2 ] [ 5.3 ] [ 5.4 ] [ 5.5 ] [ 5.6 ]

Up: Machine Learning ]

Exercise 5.3

Suppose hypothesis h commits r = 10 errors over a sample of n = 65 independently drawn examples.


  1. What is the 90% confidence interval (two-sided) for the true error rate?

    10 / 65 = 0.15
    90% interval = 0.15 +- 1.64 ( square root [ 0.15 * ( 1 - 0.15 ) / 65 ] )
    = 0.15 +- 0.073

  2. What is the 95% one-sided interval (i.e., what is the upper bound U such that errorD(h) <= U with 95% confidence)?

    upper bound = 0.15 + 0.073
    = 0.223

  3. What is the 90% one-sided interval?

    80% interval = 0.15 +- 1.28 ( square root [ 0.15 * ( 1 - 0.15 ) / 65 ] )
    = 0.15 +- 0.056
    90% upper bound = 0.15 + 0.056
    = 0.206


by: Keith A. Pray
Last Modified: July 4, 2004 7:59 AM
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