The possible outcomes here are rolling a one (we'll call it A) a two
(B) three (C) four (D) five (E) or six (F).
Let's consider that 2 (B) which turned up exactly three times.
The probability of B = Number of outcomes classified as B
__________________________________
Total number of possible outcomes
Or in this case 3 times that the B was rolled, out of a possible 6
rolls. 3/6.
Another way to put this formula is, p(B) = f/N (or probability of B
= frequency divided by the total number, N)
This is also a formula for frequency distributions, which is used in
Psychology (hypothesis testing) when individuals are sampled (random
sampled) - and the frequencies of their answers is recorded.
For example, let's say that there are 5 tokens (labeled 1, 2, 3, 4,
5) in a bag. You have 40 pulls. The # that you pulled (# times you
pulled) is recorded.
So, token 1 was pulled 2 times (2/40 total) = .05 percent of the time
token 2 was pulled 10 times (10/40 total) = .25 percent of the
time
token 3 was pulled 16 times (16/40 total) = .40 percent of the
time
token 4 was pulled 8 times
token 5 was pulled 4
If you were to graph the frequencies, 2, 10, 16, 8, 4.. you'll see
that it looks like a bell curve. low on each end & high in the
middle
You can shade (in the graph) or add up the probability of selecting
more than one. Example, the probability of pulling a 2 (.25) or a 3
(.40) is .25+.40 = .65.
A bell curve describes a normal distribution, like the one above. IQ
is also a normal distribution, if you were to graph 100 people's IQ,
you would find that not all have 100. You would find the majority had
100, but quite a few have 110 or 90, even fewer have 75 or 120. A
bell curve.
So, back to your question. If the die is rolled six times, and B (2)
is rolled 3, that's 3/6 - .50.
50% of the time, a 2 was rolled.
Now you need a z score.. a complicated formula, z scores are usually
found in the back of statistics books in tables. Look at your
textbook, if you cannot find the particular z score, I'll look for
you. Z gives you the proportion of the shaded area under that bell
(normal) curve that rolled the 2.
The 0.01 level is the p, or probability, of that occuring due to
chance. Alpha is .05, which is commonly used- this means that there is
1 chance in 20 that whatever you were looking for was found. .01 is
smaller, 1 chance in 100.
This determines the type I error as well, which is when you reject
what is actually true (as your die). a .01 level means there is only 1
chance in 100 that there is a type I error (although it is
increasingly harder to prove that your finding is significant).
I assume "die is true" means to test if it was a non-fake die.
Again, you want to visually graph the bell curve, usually the
frequencies. .01 will be in the very very upper end of the bell curve
(like an IQ of 180) the graphs really help some people to visualize
the problem. The upper and lower ends are the "regions of rejection"
where the portions contain values taht are TOO unlikely to occur by
chance (perhaps your 2). If you choose .01 level & chart those z
scores, and your 2 falls outside of this rejection area - then your
hypothesis that the die is true isn't so great.
Here are great websites that has outlined everything that I've said,
and should help you to understand the problem.
http://main.psy.ilstu.edu/faculty/cutting/psych240/chpt6.html
http://coe.sdsu.edu/ed690/modules/6-instrument/e/extend.htm
http://www.arts.uwaterloo.ca/~jfsulliv/Lectures%2012%20&%2013.html
I understand this is REALLY confusing, it's hard for me to talk about
on a computer. Also I'm very tired - and that may play apart. I
believe this is for homework, so I didn't want to THOROUGHLY &
COMPLETELY answer your question but hopefully I have given you the
tools to do so yourself.
If you have any questions or need any more help please don't hesitate
to ask me!
I'm a psych student, so this gives me extra practice!
-Rebekah |
