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
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.
