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Given repeated trials, even a sample size of 10 would start to trend towards the median in the sample. This is given repeated trials, however, and there can be substantial deviation in any one given set.
That being said, depending how you feel about the material, it probably is still in your best interest to guess.
Yeah, in the long run, random guessing would average a higher score than leaving them blank. Assuming that you know at least something about the topics being tested, you can probably respond with a more educated guess, which would tend to have you coming out even a bit ahead of random guessing.
So, I just want to confirm that my analysis is correct in the following situation:
I have a test coming up, wherein there will be a section of about 10 true or false statements. A correct answer is 2 points, an incorrect answer is 0 points, and a question left blank is 0.5 points (or 25% credit).
Am I correct in thinking that it is always better to guess? Educated guesses aside, completely random guessing would result in 50% credit over a large enough sample size, while leaving them blank is only 25%.
But then, is a sample of 10 questions way too absurdly small for any of this to matter?
Yes, it is always better to guess and you don't need to be a statistician to know that. The second statement doesn't make much sense. Yes, a sample size of 10 is small, but this doesn't make it matter less or more.
The only situation I could see to leave it blank is if you knew your current score before that section and could get an A for certain by leaving them all blank. Also, maybe the test writer is really good at leading students to choose the incorrect answer, in that case you should just flip a coin instead of guessing. I assume that both scenarios are pretty unlikely, so just study and guess if you don't know.
To put it more simply, if you can eliminate an answer on each question it's better to guess assuming there are four possible choices. The prof is a bit of an idiot for not assigning a penalty for wrong answers, IMO admitting ignorance is a boon in academia, something that should be carefully nurtured.
I'd be careful guessing on this test, I don't see why the prof would give you .5 for non-answer unless he/she were going to try hard to throw you trick questions. Or if you're going to guess, flip a coin.
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That being said, depending how you feel about the material, it probably is still in your best interest to guess.
Yes, it is always better to guess and you don't need to be a statistician to know that. The second statement doesn't make much sense. Yes, a sample size of 10 is small, but this doesn't make it matter less or more.
The only situation I could see to leave it blank is if you knew your current score before that section and could get an A for certain by leaving them all blank. Also, maybe the test writer is really good at leading students to choose the incorrect answer, in that case you should just flip a coin instead of guessing. I assume that both scenarios are pretty unlikely, so just study and guess if you don't know.
that should answer your question for you
(1/2)*2+(1/2)*0 = 1 per question , total of 10/20
Expected Value for leaving blank:
.5 per question, total of 5/20
This is assuming that you know absolutely nothing, and cannot even understand the language the quiz was written in.
Of course, there is a chance you guess terribly. If you think you are a bad guesser, we can look at the binomial distribution:
Since, as noted by Druhim, we only need 3 questions correct to do better than guessing, lets look at how probable it is you guess worse than three.
P(X < 3), where n=20 and p=.5
= 0.0002012253
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I'd be careful guessing on this test, I don't see why the prof would give you .5 for non-answer unless he/she were going to try hard to throw you trick questions. Or if you're going to guess, flip a coin.
Engineers are approximately perfect, and guaranteed to give you boilerplate advice that doesn't fit your specific issue.
Or Just ride the curve and pray the lowest score gets dropped.
wrong
he's definitely better off guessing on the ones he has no clue on