Spam filters try to sort your incoming 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 according 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 in your inbox. A high point total provides evidence that the message may be
spam. When there is sufficient 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. Complete parts (a)
through (d) below.
(a) When the filter allows spam to slip through into your inbox, what kind of error is that?
A. This is a Type I error because H0 is true, and the filter rejected it.
B. This is a Type II error because H0 is false, but the filter failed to reject it.
C. This is a Type I error because H0 is true, but the filter failed to reject it.
D. This is a Type II error because H0 is false, and the filter rejected it.
(b) Which kind of error is it when a real message gets classified as junk?
A. This is a Type II error because H0 is false, but the filter failed to reject it.
B. This is a Type II error because H0 is false, and the filter rejected it.
C. This is a Type I error because H0 is true, and the filter rejected it.
D. This is a Type I error because H0 is true, but the filter failed to reject it.