Hypothesis Testing Using Binomial Distribution Part I
Example
The result of a single experiment is seven Aa and one aa progeny observed
in a family of size eight. Our expectation is:
We want to test Ho: 1/2 Aa : 1/2 aa
We want to test HA: not the above.
The expected number of each progeny type is nx:ny. Let n=8, x=1/2,
y=1/2. We expect to observe 8 (1/2) = 4 Aa and 8 (1/2) = 4 aa progeny
when Ho is true.
| classes |
Aa |
aa |
Total |
| observed |
7 |
1 |
8 |
| expected |
4 |
4 |
8 |
How can we evaluate whether we have evidence that supports Ho? Let
us set the level of Type I error to 1/20. This means that we are willing
to erroneously reject Ho when it is true 5% of the trials. If our sample
would occur by chance in 5% or less of families, we will reject Ho.
If Ho is in fact true then we will erroneously reject Ho due to an unusual
sample of progeny in 1 of 20 experiments.
