Perhaps statistics is not for me.

#1
Please someone help! I recently answered a couple questions on a statistic test and I thought that I had answered them correctly, however the answers were marked as incorrect. I'm pretty sure that they are simple questions but I just don't get it(statistics). Here goes...


1)From a population of 200 elements, the standardard deviation is known to be 14. A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard error of the mean is_________.
The choices were: a)3, b)2(I picked this one because I thought - the standard deviation of the standard error was = 14/sqrt of the sample size 49), c)greater than 2, and d)less than 2.

2)We want to draw a simple random sample of 50 elements from a population of 500 elements. On the first selection, the probability of an element being selected is______
The choices were: a)0.100, b)0.010 c)0.001 and d)0.002. I picked a).

I missed a good deal more than these two, but I thought I had these correct.
Thanks,
SunDog
 

Dragan

Super Moderator
#2
Please someone help! I recently answered a couple questions on a statistic test and I thought that I had answered them correctly, however the answers were marked as incorrect. I'm pretty sure that they are simple questions but I just don't get it(statistics). Here goes...


1)From a population of 200 elements, the standardard deviation is known to be 14. A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard error of the mean is_________.
The choices were: a)3, b)2(I picked this one because I thought - the standard deviation of the standard error was = 14/sqrt of the sample size 49), c)greater than 2, and d)less than 2.

2)We want to draw a simple random sample of 50 elements from a population of 500 elements. On the first selection, the probability of an element being selected is______
The choices were: a)0.100, b)0.010 c)0.001 and d)0.002. I picked a).

I missed a good deal more than these two, but I thought I had these correct.
Thanks,
SunDog

What you're missing is that you have a finite population e.g. N=200 and where the sample size is n = 49 in question #1.

Thus, the standard error for the mean is equal to:

StdErr = Std/Sqrt[n] * Sqrt [(N - n) / (N - 1) ].
 
#3
In the first problem you failed to take into account the finite population correction. Your answer was correct for a population infinite in size. In a smaller population the standard deviation will be less. Got to tell ya don't loose sleep over missing this one.

On the second one it is horrible but I suspect this is the issue:

"On the first selection..."

What does that mean. I can do the math with 100% confidence. But I have a less than 100% confidence on what that means. Does that mean with the simple selection we are considering the very first one we draw? Thats what I think. But it is not accompanied by total confidence. English sucks.

Again don't loose sleep over this one. I hate these questions. I miss them too. The problem with them is that if you envision the process being asked about correctly you get it right. But if you do not envision the process correctly and envision the process as something else you answer incorrectly. I miss these ~all~ the time.

For the vast majority of statistics problems I miss it is because I thought you were asking something else. It is true. No exaggeration. If I miss it most of the time it is because something leaped into my head about the thing being asked about; but in reality it is not on the page. In fact I have learned to put a great deal of effort into parsing statistics questions and considering what else they might be asking besides what I think. That doesn't really reflect on aptitude.

I will give you an example last year: "Which of the competeing hypotheses are simple or composite and why ." I only answered for the alternative hypothesis. It is the one I commonly think of as competeing. An error. This is what I mean when you envision the wrong idea. It never even registered to me to answer for the null. Never even thought about it. So really the question was more easily worded "which of these hypothesis are composite".

And then when I did answer I wrote "the alternative is composite because there are infinite family of distributions contained within in it." And I got graded off for not putting which infinite family of distributions. Never mind it was plain as day they were normal.

But being a math guy I have a problem with superfluous information. If I write "the alternative is composite because there are infinite family of normal distributions contained within it" then I strictly speaking have become ambigious about why it is composite. Is it the number of distributions, the type of distribution (normal), or the combination of the two? From such language the grader can't be clear that I know. On the otherhand if I only state the bare minimum requirement to be composite than I am done AND unambigious.

So that question was a totally screwed. But it didn't mean I didn't know stats. It meant I had issues with the assessment process.

The point is tese arn't the sorts of errors that decide the difference. Don't dwell on them. If you make a mistake because you pictured the wrong idea move on.
 
Last edited: