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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 5.4

You are about to test a hypothesis h whose errorD(h) is known to be in the range between 0.2 and 0.6.


  1. What is the minimum number of examples ( n ) you must collect to assure that the width of the two-sided 95% confidence interval will be smaller that 0.1?

    Let E ( error D ( h ) ) = ( 0.2 + 0.6 ) / 2
    Note: I should have used 0.5
    cause the function
    f ( p ) = p ( 1 - p )
    reaches max in the interval
    [0, 1] ( and in [0.2, 0.6] )
    when p = 0.5
    = 0.4
    95% interval width = 2 * ( 1.96 * x )
    x = square root [ 0.4 * ( 1 - 0.4 ) / n ]
    for width < 0.1
    x = 0.1 / ( 1.96 * 2 ) 0.0255
    = 0.0255
    0.0255 = square root [ 0.4 * ( 1 - 0.4 ) / n ]
    0.00065025 = ( 0.4 * 0.6 ) / n
    0.00065025 = 0.24 / n
    n = 0.24 / 0.00065025
    n =
    370
    (rounded from 369.088)


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