Please answer all these questions with full working and explanation if needed fo
ID: 3070153 • Letter: P
Question
Please answer all these questions with full working and explanation if needed for that question. Pls ;)
Attempt both questions-Spam Filters and Lightbulbs. After completing THA 6, you will deepen your understanding of Type l and Type Il errors, and develop the technique of conducting a test. Spam Filters* 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 filterTrash 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 am (3015 (a)When the filter allows spam to slip through into your inbox, what kind of error is that? This is a Type I error because Ho is true, and the filter rejected it. This is a Type Il error because Ho is false, but the filter failed to reject it. This is a Type I error because Ho is true, but the filter failed to reject it This is a Type ll error because Ho is false, and the filter rejected it. A. C. D. (b)Which kind of error is it when a real message gets classified as junk? This is a Type Il error because Ho is false, but the filter failed to reject it. This is a Type Il error because Ho is false, and the filter rejected it. This is a Type I error because Ho is true, and the filter rejected it. This is a Type I error because Ho is true, but the filter failed to reject it A. (c)Some filters allow you to adjust the cutoff. Suppose your filter has a default cutoffof 50 points, but you reset it to 60. What impact does this change in the cutoff value have on the chance of each type of error A. Decreased Type I error, increased Type Il error Increased Type l error, decreased Type ll error Increased Type I error, increased Type ll error. Decreased Type I error, decreased Type Il error C. (d) Is the above change in cutoff analogous to choosing a higher or lower value of for a hypothesis test? A.A higher a, because it takes stronger evidence to classify the e-mail as spam. B. A lower a, because it takes stronger evidence to classify the e-mail as spam C. A higher a, because it takes less evidence to classify the e-mail as spam D. A lower a, because it takes less evidence to classify the e-mail as spam (1 mark each)Explanation / Answer
I will be answering the spam filters question. I request you to upload the lightbulbs question as a separate question.
(a).
B. This is a type- II error because the H0 is false, but the filter failed to reject it.
Type- II error is the probability of failing to reject the null hypothesis (or accepting it) when the null hypothesis is false. Thus, this is the correct answer.
(b).
C. This is a type- I error because the H0 is true, but the filter rejected it.
Type- I error is the probability of rejecting the null hypothesis when the null hypothesis is this. This, is also equal to the level of significance. Thus, this is the correct answer.
(c).
A. Decreased type- I error, increased type - II error
As you increase the threshold, he type- I error falls and the type- II error increases.
(d).
A. A higher alpha, since it takes stronger evidence to classify the e-mail as spam.
When the threshold increases, only a very strong evidence against the null hypothesis will lead to the rejection of the null hypothesis. Thus, we will be more confident while rejecting the null hypothesis.