Re: Correct me if I am wrong, quick question on stats mind teaser

On 30 May 2007 11:17:07 -0700, RandyThur@xxxxxxxxx wrote:

On May 30, 1:33 pm, Bruce Weaver <bwea...@xxxxxxxxxxxx> wrote:
RandyT...@xxxxxxxxx wrote:
On May 30, 10:48 am, Bruce Weaver <bwea...@xxxxxxxxxxxx> wrote:
RandyT...@xxxxxxxxx wrote:
1) If I need to know the probability that among 23 people in a class,
at least have the same birthday (assuming at least one match)
Would the answer be: 23/365 = 0.063
Try it this way: The probability of at least one match is one minus the
probability of no matches.

Much appreciated advise! I think that really clears up the trick for
me.

2) If a new large class had a test with an AVG score of 70%, STDV=10,
what are the chances of a random guy scoring 94%,
Would it be determinable? What equation would I need if the STDV does
not seen to help
Are you given any other information, such as how the scores are
distributed? I suspect you are, and that your textbook has similar
examples.

I was only given the exam average as 70% and the STDV as 10 %. and I
can't seem to figure out how to calculate the probability of someone
scoring 94%.

I'm guessing that you are supposed to assume that the scores are
(approximately) normally distributed. (The question writer will often
tell you to make that assumption.) Does this help you see what to do?

Also, the probability of the score being exactly 94% is 0. The question
ought to be asking for the probability that a randomly chosen person has
a score of 94% or higher.

The Second question then goes on to ask if 30 of the
students in the class had a mean of 75 between them, how confident
would I be (in terms of a conf. level I assume) in the refresher
course they all took as a means to do well on the exam. I seem to be
stuck, any insight.

I'm still not sure I understand what is being asked for here. I think
you're saying that 30 randomly chosen people did a refresher course,
then retook the test; and you want to test the null hypothesis that they
are a random sample from a population with a mean of 70 and SD of 10.
Does that sound right?

--
Bruce Weaver
bwea...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx/wv/bwhomedir- Hide quoted text -

- Show quoted text -

Maybe this question is not as straight forward as I thought. The
actual verbiage of the question is?

"On the average, the passing score on a exam is 70%. The Standard
Deviation of scores is 10%.what is the probability that a student
selected at random scored 94%? The student who received the 94% has
taken a refresher course to prepare for the exam, would you say the
refresher course was a success. if you selected 30 students that took
the refresher course and found that the mean was 75, how confident
(what conf. level) are you to say that the refresher course was a
success?

i am still not sure if i need to treat this as if a normally
distributon problem. or really where to start. i cant seem to find an
eqn. for probability which has only these Variables in it.


Ewart Shaw mentions "assumptions" in his post.
I had only a few courses that mentioned practicalities
like assumptions, and I never had a course that dwelt on
them as much as *I* thought appropriate. (I was already
working as a data analyst when I took most of my stat courses.)

Classroom problems are notorious for assuming heroic,
unrealistic assumptions that no experienced data analyst would
want to commit to.

About the one student....
The student who score 94% is a bit far out on the normal curve.
If he were the only student who took the refresher course,
he is marked as 'extreme' by his score; it might be another
heroic assumption to say that the course is responsible.
Unless, of course, the original course and test were unfair,
and the 'refresher' consists of providing obscure answers.

For selecting 30...
Here, you are probably expect to assume that the "30 students
that took the refresher course" scored the group average on
the first test, and that they are no different from anyone else
in motivation, etc. Also, you are not given information on
the pre-post correlation, which you would certainly want if
you were testing for a pre-post difference. Further, since the
initial group size is not stated, it apparently is assumed to be
HUGE, so that SD of 10 is a universal, population statistic.

Using all those assumptions, you can form a t-test to compare
the 75 versus a fixed score of 70, as a one-sample t-test.


http://www.pitt.edu/~wpilib/index.html
.

Relevant Pages

  • Re: Correct me if I am wrong, quick question on stats mind teaser
    ... can't seem to figure out how to calculate the probability of someone ... students in the class had a mean of 75 between them, ... you're saying that 30 randomly chosen people did a refresher course, ... the passing score on a exam is 70%. ...
    (sci.stat.edu)
  • Re: Correct me if I am wrong, quick question on stats mind teaser
    ... what are the chances of a random guy scoring 94%, ... can't seem to figure out how to calculate the probability of someone ... (The question writer will often tell you to make that assumption.) ... I think you're saying that 30 randomly chosen people did a refresher course, then retook the test; and you want to test the null hypothesis that they are a random sample from a population with a mean of 70 and SD of 10. ...
    (sci.stat.edu)