16. Spam. Spam filters try to sort your e-mails,

Chapter 21, Problem 16

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16. Spam. Spam filters try to sort your e-mails, decidingwhich are real messages and which are unwanted. Onemethod used is a point system. The filter reads each incominge-mail and assigns points to the sender, the subject,key words in the message, and so on. The higher thepoint 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 throughto your inbox, and the rest, suspected to be spam, are divertedto the junk mailbox.We can think of the filters decision as a hypothesistest. The null hypothesis is that the e-mail is a real messageand should go to your inbox. A higher point totalprovides evidence that the message may be spam; whentheres sufficient evidence, the filter rejects the null, classifyingthe message as junk. This usually works prettywell, but, of course, 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 (thats you) to adjust thecutoff. Suppose your filter has a default cutoff of 50points, but you reset it to 60. Is that analogous tochoosing a higher or lower value of for a hypothesistest? Explain.d) What impact does this change in the cutoff value haveon the chance of each type of error?