Interpreting Stemplots

Date: 05/11/98 at 05:38:58
From: Danilou
Subject: Statistics and Research Methods

I was wondering if you could help me with hypothesis testing. I don't 
really understand how you find H0 and H1. I understand that the null 
hypothesis is the same as your sample proportion or population. So in 
the instance of the stemplot with p = 0.7, then H0 is p = 0.7.

Here is my stemplot:

   Stems:0.1's   Leaves:.01's
   +|
   9|
   9|33
   9|0
   8|
   8|66
   8|
   8|33333333333
   8|000000000000000
   7|
   7|6666666666666666666666666
   7|
   7|3333333333333333333
   7|00000000000000000000000000000000000
   6|
   6|6666666666666666666666666666666666666666666
   6|
   6|333333333333333
   6|000000000000000
   5|
   5|666666666  
   5|
   5|333333
   5|0000
   4|
   -|

The stemplot is showing the distribution of the sample proportion P 
when two hundred samples of size 30 are drawn from a population with 
proportion p = 0.7.

I have worked out that H0 is p = 0.7 and H1 is p => 0.7. The 
significance level is 0.05. I do not understand the test statistic or 
its value. I also do not know the P-value, or what I am supposed to 
write for a conclusion. This computer-generated sampling distribution 
is supposed to test, at the 5% level of significance, the hypothesis 
that more than 70% of students have access to a computer at home. 

Thanks, Danilou

Date: 05/11/98 at 09:10:28
From: Doctor Statman
Subject: Re: Statistics and Research Methods

Dear Danilou,

If I understand the question, then the stemplot that you have included
represents what happened when you took a bunch of samples from a 
population that is known to have a p = 0.7. Even though you and I know 
that p = 0.7, the sample proportion for each sample does not usually 
come out to be 0.7. If you flip a coin ten times, you don't always get 
five heads, right? Same here. Even though p = 0.7, you don't always 
get 70% exactly.

The stemplot shows one collection of results sampled from your 
population where p = 0.7. If I repeated the experiment, I would get a 
stemplot that would probably look a lot like yours, but it wouldn't be 
exactly the same. Both of our stemplots would be the results of 
simulations.

If I repeated the experiment a bazillion times -- many more than would 
be practical -- I would see a regular pattern emerge. The sampling 
distribution would always be bell-shaped with a center at 0.7. So the
stemplot represents the sampling distribution from one experiment,
and it looks roughly bell-shaped. But there is a smooth curve, living
"behind the scenes," that represents what would happen if you could
repeat the experiment forever: you would get a perfect bell-shaped
curve, which represents the theoretical sampling distribution.

Hope this helps!

Statistically yours,

-Doctor Statman, The Math Forum
Check out our web site! http://mathforum.org/dr.math/