Question

In: Statistics and Probability

Spam filters try to sort your incoming e-mails, deciding which are real messages and which are...

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.

(c)           Some filters allow you to adjust the cutoff. Suppose your filter has a default cutoff of 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 II error.

B.            Increased Type I error, decreased Type II error.

C.            Increased Type I error, increased Type II error.

D.            Decreased Type I error, decreased Type II error.

(d)         Is the above change in cutoff analogous to choosing a higher or lower value of α for a hypothesis test?

A.            A higher α, because it takes stronger evidence to classify the e-mail as spam.

B.            A lower α, because it takes stronger evidence to classify the e-mail as spam.

C.            A higher α, because it takes less evidence to classify the e-mail as spam.

D.            A lower α, because it takes less evidence to classify the e-mail as spam.

Lightbulbs          

From past test records it is known that the mean lifetime of the Fillips bulbs produced is 2000 hours with a standard deviation (s) of 120 hours. The manufacturer tests a random sample of 16 light bulbs to assess the reliability of the production process with the following result (in hours).

2010

2010

1529

2450

1628

1976

1379

2068

2537

2687

2128

2156

1987

2020

1879

2356

Based on the above sample, can we say the average lifetime of Fillips lightbulbs is different from the past? Conduct the test at the significance level of 5%, using the critical value or p-value approach.

State any assumption you make in your calculations.

Notes:

Show all 6 steps.

To calculate the sample mean, you can use Excel or calculator; no working is required.

While you can get full marks for this question without a diagram, you are encouraged to draw one to help analyse the problem.

Solutions

Expert Solution

(a) Correct option : B. This is a Type II error because H0 is false, but the filter failed to reject it.

(b) Correct option : C. This is a Type I error because H0 is true, and the filter rejected it.

(c) Correct option : A. Decreased Type I error, increased Type II error.

(d) Correct option : B. lower α, because it takes stronger evidence to classify the e-mail as spam.

Lightbulbs

Null hypothesis Ho : The average lifetime of Fillips lightbulbs is not different from the past.

Alternative hypothesis H1 : The average lifetime of Fillips lightbulbs is different from the past.

Test statistic = ( sample mean - population mean ) / (population standard deviation / n0.5)

sample mean = ( 2010 + 2010 + 1529 + 2450 + ............... + 2020 + 1879 + 2356 ) / 16

sample mean = 2050

population mean = 2000

population standard deviation = 120

n = 16

Test statistic = ( 2050 - 2000) / ( 120 / 160.5) = 1.67

we are given, Alpha = level of significance = 5% = 0.05

Tabulated value ( critical value ) = Zalpha/2 = Z0.05/2 = Z0.025 = 1.96

Since, Test statistic = 1.67 < 1.96 ( critical value ), we do not reject Ho nd conclude that The average lifetime of Fillips lightbulbs is not different from the past.


Related Solutions

Spam Spam filters try to sort your e-mails, deciding which are real messages and which are...
Spam Spam filters try to sort your e-mails, deciding which are real messages and which are unwanted. One method used is a point system. The filter reads each incoming message and assigns points 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 the cutoff passes through...
If you want to know how important spam filters are to your online experience, try turning...
If you want to know how important spam filters are to your online experience, try turning them off for a day. You’ll quickly see why these tools we tend to take for granted are so essential. Generally speaking, a filtering solution applied to your email system uses a set of protocols to determine which incoming messages are spam and which are not. What the filters checks on can vary, but often they all do basically the same thing: scan header...
If you want to know how important spam filters are to your online experience, try turning...
If you want to know how important spam filters are to your online experience, try turning them off for a day. You’ll quickly see why these tools we tend to take for granted are so essential. Generally speaking, a filtering solution applied to your email system uses a set of protocols to determine which incoming messages are spam and which are not. What the filters checks on can vary, but often they all do basically the same thing: scan header...
(15) Imagine the time it takes your boss to answer your e-mails is uniformly distributed from...
(15) Imagine the time it takes your boss to answer your e-mails is uniformly distributed from 15 – 120 minutes. What is the average time it takes her to respond? What is the standard deviation for her response time? (16) What is the probability your boss will respond to an e-mail within one hour? (17) What is the probability it will take your boss longer than 30 minutes to respond? (18) What is the probability your boss will respond to...
Which of the following business messages would not use the direct strategy? a. An e-mail message...
Which of the following business messages would not use the direct strategy? a. An e-mail message to a staff introuducing a new employee b. A letter a customer denying his or her request for credit c. A letter to a coworker congratulating him or her on a recent promotion d. An oral presentation detailing the specifics of a new company wellness initiative
Pick one or two real cases happened in your real life, try to find and analyze...
Pick one or two real cases happened in your real life, try to find and analyze the economic law issues in them by using the rules we mentioned in Economic Law.
A. Explain your reasons for deciding which is better: improve the processor or improve the algorithm?...
A. Explain your reasons for deciding which is better: improve the processor or improve the algorithm? Use the following facts in your consideration:        ❖ PC / home computer executes 10 ^ 8 comparisons per second        ❖ Supercomputer executes 10 ^ 12 comparisons per second        ❖ The complexity of insertion sort O (n ^ 2) and quick sort 0 (n log n). B. There are two algorithms (A and B) that can be used to solve a given...
Design a program which uses functions to sort a list and perform a binary search. Your...
Design a program which uses functions to sort a list and perform a binary search. Your program should: Iinitialize an unsorted list (using the list provided) Display the unsorted list Sort the list Display the sorted list. Set up a loop to ask the user for a name, perform a binary search, and then report if the name is in the list. Use a sentinel value to end the loop. Do not use the Python built in sort function to...
a) Which of the following reactions occur when (E,Z,E)- octa-2,4,6-triene is heated? Circle your choice: -...
a) Which of the following reactions occur when (E,Z,E)- octa-2,4,6-triene is heated? Circle your choice: - Diels-Alder -Cycloaddition - Cope rearrangement -Electrocyclic -Sigmatropic b) Sketch the MAJOR product that is formed when (E,Z,E)-octa-2,4,6-triene is heated. Be sure clearly show features such as the correct regio- and stereochemistry.
In your case study, discuss the following aspects of the real company in the world which...
In your case study, discuss the following aspects of the real company in the world which must have offering bonds. you can chose any company which you like. 1. Provide a brief introduction of the company, including its name, headquarters, products/services offered, and approximate net worth. 2. Explain how the company is doing with respect to the ratios. Consider debt-to-equity, return on equity, current and quick ratio, working capital ratio, price earnings ratio, and the earnings per share. (chap 2)...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT