Associated Topics || Dr. Math Home || Search Dr. Math

### 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/
```
Associated Topics:
High School Statistics

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search