In the following scenario, please clarfy the null and alternate
hypotheses:  A substance abuse treatment center advertises that 85% of
the patients that complete their program do not drink or use drugs in
a one-year period after completion.  Within the last five years,
management has had reason to believe that this figure is no longer
accurate. A survey of 50 patients, who completed the program between 1
and 2 years ago, was done.  It was found that 38 of them continued to
stay clean/sober during that period of time.  Is the advertised
percentage (85%) of clients staying clean/sober within a 2 year period
of time following the the completion of the program correct?  H[a] < 
H[o].  Please define the parameter in each, say mu.

Hi again boobee,

OK, lets start with definitions for these two terms:

Null Hypothesis - the statement tentatively assumed true in the
hypothesis testing procedure

Alternative Hypothesis - the statement concluded to be true if the
null hypothesis is rejected

**It is VERY important to note that the null hypothesis and
alternative hypothesis are mutually exclusive and completely
exhaustive. In other words, it is not possible for both to be true,
and it is not possible for both to be false.

There are three generally used types of hypotheses:

RESEARCH HYPOTHESES

In this case, the alternative hypothesis is stating what the research
is trying to conclude. THe null hypothesis is the opposite of the
alternative hypothesis.

CLAIM VALIDITY

In this case, the null hypothesis equals the claim being made, and the
alternative hypothesis is the opposite the the nll hypothesis. We
originally assume that all claims being made are true and then try to
test to see if they are or not.

DECISION-MAKING

The null hypothesis is the condition corresponding to a "yes"
condition, and the alternative hyposthesis is the condition
corresponding to a "no" condition. We originally assume that the
decision should be yes, and then use the test to see if this is
correct or not.



Applying the above to your question, we can see that we are using
hypothesis testing to measure the validity of the claim. The claim
states:

"85% of the patients that complete their program do not drink or use
drugs in
a one-year period after completion"

Since we assume all claims are true to begin with, our null hypothesis
states:

"85% or more of the patients that complete their program do not drink
or use drugs in a one-year period after completion"

Then, since we know that the two hypotheses must be mutually exclusive
and collectively exhaustive, it follows that the alternative
hypothesis states:

"Less than 85% of the patients that complete their program do not
drink or use drugs in a one-year period after completion"

Hope that helps....let me know if you have any problem understanding
the information above.

Cheers!

answerguru-ga

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Request for Answer Clarification by boobee-ga on 25 Sep 2002 17:31 PDT

Can you please define the parameter.

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Clarification of Answer by answerguru-ga on 25 Sep 2002 23:51 PDT

Hi boobee,

I wasn't sure if you wanted the parameter or not...anyways here it is:

Since we are measuring a population proportion we can use a confidence
interval to make the decision of whether to accept/reject the null
hypothesis. It is standard to do this at a 95% level of confidence
(though you do it at any level you like).

The formula for an interval estimate of population proportion is:

p +/- Z(alpha/2)sqrt(p(1-p)/n)

The (alpha/2) is a subscript of Z which results in a value consistent
with a normal distribution for the given level of confidence. Since we
are using 95%, then there is a 5% chance our value will not fall
within the appropriate range. Since the distribution is symmetric, we
divide by 2 to get a 2.5% (or 0.025). The Z value corresponds to the
number of standard deviations beyond the mean that the interval
extends. In this case the value equals 1.96 (this was obtained by
looking up a normal distribution table of Z values).

So plugging the values into the formula:

0.76 +/- 1.96*sqrt(0.76*0.24/50)

0.76 +/- 1.96*sqrt(0.003648)

0.76 +/- 0.118

Therefore our interval at a 95% level of confidence is [0.64, 0.88].
This is our parameter that is required to make a decision. Since the
85% claim is within the interval, it is safe to say that the null
hypothesis is correct.

Good luck!

answerguru-ga

Great answer as usual