Really?
So,
p = 82,500 / 200,000,000 = 0.0004125
n = 5000
p * n = 2.0625
The most likely outcomes would be 1 or 2 positives.
Here follows the probabilities (binomial distributions) for getting x positives (or more):
Code:
>=x probability
1 0.8729183528
2 0.6107042921
3 0.3402385566
4 0.1542910381
5 0.0584298337
6 0.0189024160
7 0.0053228521
8 0.0013248828
9 0.0002951746
10 0.0000594802
11 0.0000109357
12 0.0000018480
13 0.0000002889
14 0.0000000420
15 0.0000000057
16 0.0000000007
17 0.0000000001
18 0.0000000000
Do I need to go on? The probability of even getting 20 or more positives is less than 1 in 9 trillion, "if it was conducted perfectly".
We had
over 50 positives.
Are you suggesting that would not be statistically significant?