Spam Spam filters try to sort your e-mails, deciding whichare real messages and which are unwanted. One methodused is a point system. The filter reads each incominge-mail and assigns points to the sender, the subject, keywords in the message, and so on. The higher the point total,the more likely it is that the message is unwanted. The filterhas a cutoff value for the point total; any message ratedlower than that cutoff passes through to your inbox, and therest, suspected to be spam, are diverted to the junk mailbox.We can think of the filter’s decision as a hypothesistest. The null hypothesis is that the e-mail is a real messageand should go to your inbox. A higher point total provides evidence that the message may be spam; when there’s suf-ficient evidence, the filter rejects the null, classifying the message as junk. This usually works pretty well, but, ofcourse, sometimes the filter makes a mistake.a) When the filter allows spam to slip through into yourinbox, which kind of error is that?b) Which kind of error is it when a real message getsclassified as junk?c) Some filters allow the user (that’s you) to adjust thecutoff. Suppose your filter has a default cutoff of50 points, but you reset it to 60. Is that analogous to choosing a higher or lower value of a for a hypoth-esis test? Explain. d) What impact does this change in the cutoff value haveon the chance of each type of error?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Spam Spam filters try to sort your e-mails, deciding which
are real messages and which are unwanted. One method
used is a point system. The filter reads each incoming
e-mail and assigns points to the sender, the subject, key
words in the message, and so on. The higher the point total,
the more likely it is that the message is unwanted. The filter
has a cutoff value for the point total; any message rated
lower than that cutoff passes through to your inbox, and the
rest, suspected to be spam, are diverted to the junk mailbox.
We can think of the filter’s decision as a hypothesis
test. The null hypothesis is that the e-mail is a real message
and should go to your inbox. A higher point total provides

evidence that the message may be spam; when there’s suf-
ficient evidence, the filter rejects the null, classifying the

message as junk. This usually works pretty well, but, of
course, sometimes the filter makes a mistake.
a) When the filter allows spam to slip through into your
inbox, which kind of error is that?
b) Which kind of error is it when a real message gets
classified as junk?
c) Some filters allow the user (that’s you) to adjust the
cutoff. Suppose your filter has a default cutoff of
50 points, but you reset it to 60. Is that analogous

to choosing a higher or lower value of a for a hypoth-
esis test? Explain.

d) What impact does this change in the cutoff value have
on the chance of each type of error?

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