
Project 5: Evaluating Hypotheses
Exercise 5.4
You are about to test a hypothesis
h whose error_{D}(h)
is known to be in the range between 0.2 and 0.6.

What is the minimum number of examples ( n ) you must collect to
assure that the width of the twosided 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)

