Number 2 may very well be statistically significant if there is a low rate of fire/strike in ICE cars and a high rate in Tesla. Even with only 3 samples, we may be able to say there is statistical significance. Now, I agree that 3 is a low number and thus error in the calculation will be high. That does not mean, however, that we still cannot reach the 95% confidence interval most often used to determine significance. If I had more time, I'd try to work the calculation out. Maybe this weekened. It would certainly be a tentative calculation and one that, if being published in a journal, would require more support. However, there are ways to determine if there is a problem and that is where the NHTSA comes in.
I will leave it to BillHamp to calculate statistical significance as I honestly couldn't figure out how to calculate it or test for it. However, I'd like to answer a different question.
QUESTION: Based on the given sample size, what is the margin of error?
ANSWER: Let's calculate the margin of error.
Disclaimer: I'm not a statistics guy by any stretch, indeed, needed to google the formula to get the answer.
Source:
http://www.dummies.com/how-to/content/how-to-calculate-the-margin-of-error-for-a-sample0.html
Assumptions: For this argument we will assume 3 fires per 19000 Model S. We will assume confidence interval of 95% is desired as per BillHamp's post, and as it seems to be a rather common confidence interval.
Calculations:
Sample Proportion (p) = 3/19000 = 0.000158 = 0.0158%
z* (assuming normal distribution) = 1.96 <---- this number taken from the normal distribution table of z* values
Sample Size (n) = 19000
Margin of Error = z* ( sqrt ( ( p ( 1 - p ) / n )
Margin of Error = 1.96 ( sqrt ( ( 0.000158 ( 1 - 0.000158) / 19000 )
Margin of Error = 1.96 ( sqrt ( 0.000000008309 ) )
Margin of Error = 1.96 ( 0.0000912 )
Margin of Error = 0.000179
Margin of Error = 0.0179%
Therefore, you can conclude with 95% confidence that 0.0158% of Model S cars catch fire, plus or minus 0.0179%
Or, another way of looking at it is you can conclude with 95% confidence that somewhere between -0.0021% and 0.0337% of Model S cars catch fire.
My take: Looks to me that we still have a pretty wide margin of error (so as everyone has been suggesting, we need a larger sample size before we really know what's going on). Based on this calculation, for the next 19000 cars we should expect anywhere between approximately 0 and 6 fires with 95% confidence.