Chapter 21, Problem 16E

(a)

To determine

To explain when the filter allows spam to slip through into your inbox which kind of error is that.

Answer to Problem 16E

It is a Type II error.

Explanation of Solution

It is given in the question that spam filter try to sort your e-mails deciding which are real messages and which are unwanted. The filter reads each incoming e-mail and assigns points to the sender, the subject, key words in the message and so on. Thus, when the filter allows spam to slip through into your inbox, then it is a Type II error as the null hypothesis was not rejected even though it was false.

(b)

To determine

To find out which kind of error is it when a real message gets classified as junk.

Answer to Problem 16E

It is a Type I error.

Explanation of Solution

It is given in the question that spam filter try to sort your e-mails deciding which are real messages and which are unwanted. The filter reads each incoming e-mail and assigns points to the sender, the subject, key words in the message and so on.Thus, when a real message gets classified as junk then it is a Type I error because the null hypothesis was incorrectly rejected when it was true.

(c)

To determine

To explain is that analogous to choosing a higher or lower value of $\alpha$ for a hypothesis test.

Answer to Problem 16E

It is lower.

Explanation of Solution

It is given in the question that spam filter try to sort your e-mails deciding which are real messages and which are unwanted. The filter reads each incoming e-mail and assigns points to the sender, the subject, key words in the message and so on.Thus, it is analogous to choosing a lower value of $\alpha$ for a hypothesis test because it takes more evidence to classify the email as spam.

(d)

To determine

To explain what impact does this change in the cut-off value have on the chance of each type of error.

Explanation of Solution

It is given in the question that spam filter try to sort your e-mails deciding which are real messages and which are unwanted. The filter reads each incoming e-mail and assigns points to the sender, the subject, key words in the message and so on.Thus, the impact does this change in the cut-off value have on the chance of each type of error is that the risk of a Type I error decreases but the risk of a Type II error increases because the probability of a Type I error as alpha while the probability of a Type II error is $1-\alpha$ .