Re: Critical value and test statistic

Ethan.Johnsons@xxxxxxxxx wrote:
Old Mac User wrote:
It's impossible to answer this question unless you supply more
information.
For instance, if you are working with the frequency of defectives in a
sample
(sample is n = 5000...???) then it may be possible to move forward with
this.
But not with a t-ratio test. We need to know more about what kind of
data you
are dealing with and the context of how it came to be. OMU



Ethan.Johnsons@xxxxxxxxx wrote:
The general population has the mean (5/1000); and the test sample has
(15/5000).
However, we don't know the sd. In this case, how to calculate t value?

If I use the critical-value method with α =0.05, then I come up with
the critical value, -1.645158

My question is how to calculate t value without knowing the sd at all?

The formula is t = (x bar - mu 0) / (sd/sqrt(n)).
so, it could be:

(5/1000 - 15/5000)
--------------------------
sd /sqrt(5000)

thx

ej

The context is:
"Suppose the incident rate of MI (myocardial infraction) per year was 5
per 1000 men in 1990. To look at the changes in incidence over time,
5000 men were followed for 1 year starting in 2000. 15 new cases of MI
were found.", and we know α =0.05 for the critical-value method.
and I am trying to test if the incident rate of MI has changed from
1990 to 2000.

To test whether the rate in the 5000 men was the same as the 1990 rate is easy: I would take the 1990 rate as fixed (this isn't exactly right, but the standard error is probably rather complex), and ask whether the rate from the 5000 men could come from a binomial distribution with a mean p equal to the 1990 value. You'll inflate significance slightly, but hopefully the result will be clear enough.

As to whether the rate has changed, you would need to know about the 5000 men followed: were they a random sample from the population? Pick a bunch of 20 year old men, and the rate in the sample will be much lower, even if the rate in the population has increased.

HTH

Bob

--
Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland

Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
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