Spam filters attempt to sort e-mails, deciding which are real messages and which are unwanted. One method used is point system. Filter reads each incoming e-mail and assigns points to sender, the subject, key words in message, and so on. Higher point total, the more likely it is that message is unwanted. Filter has cutoff value for point total; any message rated lower than that cutoff passes through to inbox, and rest, suspected to be spam, are diverted to junk mailbox.

We can think of filter's decision as hypothesis test. Null hypothesis is that e-mail is the real message and must go to your inbox. Higher point total gives evidence that message may be spam; when there's sufficient evidence, filter rejects null, classifying message as junk. This generally works pretty well, but, of course, sometimes filter makes a mistake.

a) When filter permits spam to slip through into your inbox, which type of error is that?
b) Which type of error is it when the real message gets classified as junk?
c) Some filters permit the user (that's you) to adjust cutoff. Assume your filter has default cutoff of 50 points, but you reset it to 60. Is that analogous ot choosing higher or lower value of α for hypothesis test? Describe.
d) What impact does this change in cutoff value have on chance of each type of error?