
Project 5: Evaluating Hypotheses
Exercise 5.3
Suppose hypothesis h commits r = 10 errors over
a sample of n = 65 independently drawn examples.

What is the 90% confidence interval (twosided) 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


What is the 95% onesided interval
(i.e., what is the upper bound U such that
error_{D}(h) <= U with
95% confidence)?
upper bound

=

0.15 + 0.073


=

0.223


What is the 90% onesided 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


