[Order] Merry Testmas!

[Yvain Wintersong]

Testmas is a holiday celebrated by, of course, taking tests. This is sort of an IQ test, and sort of a list of trick questions - but more than that, it's a logical pitfall test. It's laden with extremely common mistakes people make when reasoning, and you will get points for every logic error you avoid.

There are only thirteen questions; most of them questions are taken either from the Overcoming Bias blog or studies in cognitive psychology. When everyone who wants to has taken the test (you can post answers below), I'll explain the study that each question comes from, what it proves, and, of course, what the correct answer is.

I don't have any prizes in mind (besides more closely approaching Truth), but if the person who does the best can think of something he/she wants, I might give it to him/her.

1. You have a weighted coin that comes up heads 66% of the time and tails 33% of the time. You flip it twenty times. Which of the following sequences do you think is most likely to exist among those twenty flips?

a) HHHHHH
b) HHTHHT
c) HTTTTH
d) TTTTTT
e) All are equally likely

2. Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Rank the following statements from most probable to least probable:

1. Linda is a teacher in an elementary school.
2. Linda is active in the feminist movement.
3. Linda is a bank teller.
4. Linda works in a bookstore and takes yoga classes.
5. Linda is a bank teller and is active in the feminist movement.
6. Linda is an insurance salesman.

3. Consider a person randomly chosen from the phone book named John. We investigate John's personality and find that he is quiet, bright, and likes poetry and classical music. Which of the following is MOST likely true?

a) John is a truck driver
b) John is a professor at an Ivy League school
c) Both of these are equally likely

4. A man has a machine with a button on it. If you press the button, there is a one in five hundred thousand chance that you will die immediately; otherwise, nothing happens. He offers you some money to press the button once. What do you do? Do you refuse to press it for any amount? If not, how much money would convince you to press the button?

5. A cab was involved in a hit-and-run accident. Two cab companies serve the city: the Green, which operates 85% of the cabs, and the Blue, which operates the remaining 15%. A witness identifies the hit-and-run cab as Blue. When the court tests the reliability of the witness under circumstances similar to those on the night of the accident, he correctly identifies the color of the cab 80% of the time and misidentifies it 20% of the time. So...

a) Believe him. The cab was likely blue
b) Don't believe him. The cab was probably green.
c) The cab had an equal chance of being either blue or green.
d) There's no way to tell the probability from this information.

6. You're a politician working on the budget. Which of these seems most worthy of funding?

a) An special team to stop terrorist attacks. Policy analysts say it will stop 95% of planned attacks on your country's soil.
b) Research for curing cancer. Scientists think it will save the lives of 20% of cancer patients.
c) Funding more policemen and detectives. This could cut the homicide rate by 66%

7. Which of these are you most likely to die from?

a) Terrorism!!!
b) Earthquake!!!
c) Asteroid strike!!!
d) Snakebite/spider bite!!!
e) All approximately equal!!!

8. In a standard novel, which of the following would you expect to see most often?

a) Words beginning with the sequence "fij"
b) Words ending with the letter "g"
c) Words beginning with the letter "q"
d) Words ending with the sequence "ing"

9. And which are there more of?
a) words beginning with K, like "king"
b) words with k as the third letter, like "rake"?

10. Counting from one to a million, which are there most of:
a) Numbers with "3" as the last digit
b) Numbers with "9" as the last digit
c) Numbers with either "2" or "5" as the last digit
d) All the same.

11. I am teaching a class, and I write upon the blackboard three numbers: 2-4-6. "I am thinking of a rule," I say, "which governs sequences of three numbers. The sequence 2-4-6, as it so happens, obeys this rule. Each of you will find, on your desk, a pile of index cards. Write down a sequence of three numbers on a card, and I'll mark it "Yes" for fits the rule, or "No" for not fitting the rule. Then you can write down another set of three numbers and ask whether it fits again, and so on. When you're confident that you know the rule, write down the rule on a card. You can test as many triplets as you like." Here's the record of one student's guesses:

4, 6, 2 No
4, 6, 8 Yes
10, 12, 14 Yes

At this point the student wrote down his guess at the rule. What do you think the rule is? Would you have wanted to test another triplet, and if so, what would it be?

12. For the following, you have my guarantee that they are NOT trick questions. They are simple questions of knowledge. The catch is that after each answer, please list a 0-100% confidence level in your answer. 100% means you are absolutely sure your answer is right. 0% means you are absolutely sure your answer is wrong. 50% means you think there's a 50-50 chance your answer is right. For example, if the question was
"What's 1+1?", your confidence should hopefully be near 100%.

1. What's the biggest city (including metropolitan area) in the world?
CONFIDENCE LEVEL:
2. What was the largest empire in history?
CONFIDENCE LEVEL:
3. Now that Pluto's no longer a planet, which planet is smallest?
CONFIDENCE LEVEL:
4. Rank these religions from most to least followers: Christianity, Judaism, Islam, Hinduism
CONFIDENCE LEVEL:

13. Same thing, only this time, you're given the answers. It's from a famous study of US World War II soldiers, along with a summary of historian Arthur Schlesinger's comments on what he thought the reasons for each result were. Please predict how confident you are that you WOULD have chosen the correct answer if you hadn't already known what it was.

Q: Did better educated or less educated soldiers adjust better to war?
A: Better educated soldiers suffered more adjustment problems than less educated soldiers, because intellectuals were less prepared for battle stresses than street-smart people.
CONFIDENCE LEVEL:

Q: Did Northerners or Southerners adjust to the climate in the Pacific better?
A: Southern soldiers coped better, because Southerners were more accustomed to hot weather.
CONFIDENCE LEVEL:

Q: Did white or black privates work harder to get promoted?
A: Black privates were more eager to be promoted, perhaps because the military was one of only a few jobs with almost equal opportunities.
CONFIDENCE LEVEL:

Q: Did blacks prefer to work with whites from the North or the South?
A: Most blacks were Southerners, and preferred Southern to Northern white officers because Southern officers were more experienced and skilled in interacting with blacks.
CONFIDENCE LEVEL:

Q: Were soldiers more eager to return home during or after the fighting?
A: They were more eager to return during fighting, as they knew they were in mortal danger.
CONFIDENCE LEVEL:

[benkern]

1e
2 Equally likely, or if this is not an option, 1,2,3,4,5,6
3c
4 Would not press
5c
6c
7d
8b
9a
10d
11
12; 1 Tokyo, 20%; 2 Mongolian Empire, 50%; 3 Pluto, 100%; 4 Christianity, Islam, Hinduism, Judaism (Sorry Scott! :P), 50%
13; 1 50%; 2 10%; 3 75%; 4 20%; 5 10%

This is probably the stupidest thing I have done so far this year. At least, it felt like it I wasted the most time on it. And that's competing with IT coursework.

Edit: Maybe I lose then, because I did all the questions.

[Neike Taika-Tessaro]

Oh, ya-a-a-ay! Tests!
*plunges into for the hell of it*

#1: a
#2: 3, 4, 6, 2, 1, 5, though the differences are so minute I kept nudging things around.
#3: c
#4: refuse (and ask for the purpose :-P)
#5: a
#6: b
#7: d
#8: b
#9: b
#10: c
#11: I think the rule he wrote down was "even numbers following: a, a+2, a+4". I don't know what the rule is. I would have liked to test 5, 7, 9, and 78, 80, 82 (or something similarly large). Possibly more.
#12:

1. What's the biggest city (including metropolitan area) in the world? India's capital city which I forgot the name of
CONFIDENCE LEVEL: 40%
2. What was the largest empire in history? I don't know, but if I had to guess, I would assume it to be some Asian one. I'm really bad at history, though, so I'm happier saying "I don't know".
CONFIDENCE LEVEL: -
3. Now that Pluto's no longer a planet, which planet is smallest? Mercury
CONFIDENCE LEVEL: 95%
4. Rank these religions from most to least followers: Christianity, Judaism, Islam, Hinduism: Hinduism, Islam, Judaism, Christianity.
CONFIDENCE LEVEL: 90%

#13:

Q: Did better educated or less educated soldiers adjust better to war?
A: Better educated soldiers suffered more adjustment problems than less educated soldiers, because intellectuals were less prepared for battle stresses than street-smart people.
CONFIDENCE LEVEL: 60%

Q: Did Northerners or Southerners adjust to the climate in the Pacific better?
A: Southern soldiers coped better, because Southerners were more accustomed to hot weather.
CONFIDENCE LEVEL: 95%

Q: Did white or black privates work harder to get promoted?
A: Black privates were more eager to be promoted, perhaps because the military was one of only a few jobs with almost equal opportunities.
CONFIDENCE LEVEL: 95% (without the "perhaps" part, at any rate.)

Q: Did blacks prefer to work with whites from the North or the South?
A: Most blacks were Southerners, and preferred Southern to Northern white officers because Southern officers were more experienced and skilled in interacting with blacks.
CONFIDENCE LEVEL: 50% (= I would have flipped a coin :P)

Q: Were soldiers more eager to return home during or after the fighting?
A: They were more eager to return during fighting, as they knew they were in mortal danger.
CONFIDENCE LEVEL: 0%

Wait, how are you supposed to be able to focus on anything other than fighting while you're in the middle of battle? Or am I misunderstanding that last question - as in, do they just mean during periods of vendetta, rather than of actual, right-there-and-then combat?

Edit - Okay, I'm noticing that my wagering that the length of the sequence would be more important than the amount of heads was incorrect in #1 - it is actually the first sequence (5.4% chance), not the third sequence, though that's the 'close' second with 3.1%.

Edit #2 - See below.

[Yvain Wintersong]

Yvain realizes he did one wrong himself, and quietly edits it with a chagrined look on his face.

[Neike Taika-Tessaro]

Well if you're going to redo the question, I'm going to redo the answer. Nyah. *edit*

[Ari Rahikkala]

1. a
2. 1, 2, 3, 4, 5, 6, but only because insurance salesmen are evil .
3. a
4. I'd do it for a couple of hundred euros.
5. c (0.586 is not nearly enough of a probability to be admissible in court)
6. b
7. d
8. b
9. b
10. c
11. Each number is two larger than the one before. The triplet I'd like to test is 2-4-5.

12:

1. Is this by population or by area? If it's by population, I'll go with, uhh... New York, with 40% confidence.
2. British Empire, 90% confidence.
3. Mercury, 99.99% confidence.
4. Christianity, Hinduism, Islam, Judaism. 30% confidence, mostly because I had to flipflop between Hinduism and Islam...

13:

1. 10%
2. 40%
3. 5%
4. 20%
5. 5%

[Andreas the Wise]

1 b (though I'm so tempted to use Hypothesis testing, having done it in maths recently to confirm)
2 This is logic? 2,4,1,5,3,6
3 c
4 Refuse, but only cause I'm trying to work out the trick. Otherwise, the point where the utilit overcomes the risk ... say, 100 billion should be enough.
5 c (though I should sit down and Hypothesis test it ...)
6 b (closely followed by c)
7 d, since I live in Australia ...
8 d, though there's bound to be a trick ...
9 b
10 c
11 Rule is add onto the previous number by two. More tests - depends on how tricky the teacher is. Wait, it's you? YES, just to check if you can go 3 5 7 (ie not even numbers)
12. 1. What's the biggest city (including metropolitan area) in the world?
Beijing? 20%
2. What was the largest empire in history?
Mongols, 90%
3. Now that Pluto's no longer a planet, which planet is smallest?
Mercury, 99%
4. Rank these religions from most to least followers: Christianity, Judaism, Islam, Hinduism
Christianity, Islam, Hinduiusm, Judaism, 90%
13 (note I tried to answer each question before reading the answer, so I have a good idea of what I would have answered)
Q: Did better educated or less educated soldiers adjust better to war?
A: Better educated soldiers suffered more adjustment problems than less educated soldiers, because intellectuals were less prepared for battle stresses than street-smart people.
CONFIDENCE LEVEL: 90%
Q: Did Northerners or Southerners adjust to the climate in the Pacific better?
A: Southern soldiers coped better, because Southerners were more accustomed to hot weather.
CONFIDENCE LEVEL: 95%
Q: Did white or black privates work harder to get promoted?
A: Black privates were more eager to be promoted, perhaps because the military was one of only a few jobs with almost equal opportunities.
CONFIDENCE LEVEL: 80%
Q: Did blacks prefer to work with whites from the North or the South?
A: Most blacks were Southerners, and preferred Southern to Northern white officers because Southern officers were more experienced and skilled in interacting with blacks.
CONFIDENCE LEVEL: 30%
Q: Were soldiers more eager to return home during or after the fighting?
A: They were more eager to return during fighting, as they knew they were in mortal danger.
CONFIDENCE LEVEL: 40%

[Maksym Hadjimehmetov]

1.) b
2.) 2,3,1,5,4,6
3.) c
4.) enough for my relatives to sue the bástard on my behalf posthumously
5.) d
6.) b
7.) e
8.) b
9.) b
10.) d
11.) 2-4-5
12.)

1. What's the biggest city (including metropolitan area) in the world?
Mexico City, I believe (60%)
2. What was the largest empire in history?
Mongol Empire, including all splinter states like Ilkhans, Golden Horde etc (75%)
3. Now that Pluto's no longer a planet, which planet is smallest?
Mercury? (40%)
4. Rank these religions from most to least followers: Christianity, Judaism, Islam, Hinduism
Christianity, Islam, Hinduism, Judaism (95%)

13.)
Q: Did better educated or less educated soldiers adjust better to war?
A: Better educated soldiers suffered more adjustment problems than less educated soldiers, because intellectuals were less prepared for battle stresses than street-smart people.
CONFIDENCE LEVEL: 40%


Q: Did Northerners or Southerners adjust to the climate in the Pacific better?
A: Southern soldiers coped better, because Southerners were more accustomed to hot weather.
CONFIDENCE LEVEL: 30%

Q: Did white or black privates work harder to get promoted?
A: Black privates were more eager to be promoted, perhaps because the military was one of only a few jobs with almost equal opportunities.
CONFIDENCE LEVEL: 70%

Q: Did blacks prefer to work with whites from the North or the South?
A: Most blacks were Southerners, and preferred Southern to Northern white officers because Southern officers were more experienced and skilled in interacting with blacks.
CONFIDENCE LEVEL: 15%

Q: Were soldiers more eager to return home during or after the fighting?
A: They were more eager to return during fighting, as they knew they were in mortal danger.
CONFIDENCE LEVEL: 50%

[Liam conToketi]

1.) c
2.) They are all equally probable
3.) c
4.) $50 would be enough
5.) c (especially if it was night)
6.) c
7.) c
8.) c
9.) b (because there is no c, which means neither will be the correct answer)
10.) c
11.) I would first test the sequences 3-5-7, 2-3-4, and 6-4-2
12.)
---> a.) Tokyo, 75%
---> b.) Mongol, 80%
---> c.) Mercury, 99.99%
---> d.) Christianity, Islam, Hinduism, Judaism, 99.99%
13.)
---> a.) 50%
---> b.) 40%
---> c.) 10% (since most of everyone were probably more worried about living)
---> d.) 55%
---> e.) 15%