Suppose that I have a pool of fish that have a variety of attributes. Of the total in the pool, some percentage have attribute G.
All of the fish in the pool are tagged with either tag A (10%), tag B (40%), or tag C (50%). Furthermore, we know that G is not evenly distributed among the three tags. The distribution of G is like this: 70% are A tags, 30% are B tags, and 0% are C tags.
Now, if I take a sizeable random sample from this population, the number of tags should match the ratio at which they appear in the population, so the number of that sample that is G seems like it should be:
Number sampled * ((0.1 * 0.7) + (0.4 * 0.3) + (0.5 * 0.0))
The first question is whether this is right?
The second question is making things a bit more complicated. Suppose we know that only a portion of the fish are tagged, but that ALL of the G fish are tagged and tagged at the ratio mentioned above, and that the ONLY fish sampled are tagged fish, such that they come from the tagged pool and don't include any of the untagged fish.
As I write this, it seems like the exact same equation would be the right one. In this second scenario, it seems like the untagged fish can be ignored, because the sample is taken only from the tagged fish rather than the total population of fish.
Is that right?
All of the fish in the pool are tagged with either tag A (10%), tag B (40%), or tag C (50%). Furthermore, we know that G is not evenly distributed among the three tags. The distribution of G is like this: 70% are A tags, 30% are B tags, and 0% are C tags.
Now, if I take a sizeable random sample from this population, the number of tags should match the ratio at which they appear in the population, so the number of that sample that is G seems like it should be:
Number sampled * ((0.1 * 0.7) + (0.4 * 0.3) + (0.5 * 0.0))
The first question is whether this is right?
The second question is making things a bit more complicated. Suppose we know that only a portion of the fish are tagged, but that ALL of the G fish are tagged and tagged at the ratio mentioned above, and that the ONLY fish sampled are tagged fish, such that they come from the tagged pool and don't include any of the untagged fish.
As I write this, it seems like the exact same equation would be the right one. In this second scenario, it seems like the untagged fish can be ignored, because the sample is taken only from the tagged fish rather than the total population of fish.
Is that right?