You have misquoted me and out of context.
Two hundred is accepted as the statistically random number of samples, or subjects, to aim for. This irons out results that are outwith ± 2.15 standard deviations. Unless you have enough samples, you will have difficulty calculating the 98% siginificancce level.
For example, I might set out to discover average height in London, and the first 20 people I pick out at random could all be over 6' tall. Do you understand the need to sample a few more than that?
I am confused by your statistics. In my research, one often has to calculate in advance how many "n's" (replicates, samples, etc.) one would need in an experiment to get a certain statistically acceptable error. Of course the number of n's required depends on the distribution of the population, the reproducabilty of the experimental replicates, and on the confidence level that would be acceptable to the researcher (typically for a p=< 0.05). For most experiments, n is far less than 200! Often one can do an n=3 and get results that are statistically quite different from the null hypothesis by a p=<0.05 or much less (the smaller the p value the more confidence in the result not being due to random chance).
In your example, if you wished to calculate the average height of a Londoner, and you only measured 20, you could probably say that the height of a typical Londoner is within a range from 3 feet to 8 feet with a p value of =<0.05. But even 20 truly random samples would make a height of 1 foot very unlikely. The more people you measured the more accurately you could estimate the average height and the typical range of heights, but you wouldn't need to do 200 to simply rule out 1 foot as a typical height. You wouldn't even need to do 20.
This is generally true with all experimental data, and this type of statistical analysis is usually published with the data. In the case of the Nature paper, they indicated that the statistical error of their dates, even when considered lab by lab, was plus or minus less than 100 years with a p=<0.05. This did not require anywhere near the 200 samples you propose here. The possibility that these results could have been obtained by random chance from a 30 AD object is probably far less than one in a million (sorry, I haven't calculated the exact number yet).
Perhaps 200 more analyses might narrow the date a bit further, perhaps to +/- 10 years. But it would still come out as solidly Middle Ages.
Even the choice of "200" seems totally arbitrary. In science one first calculates the acceptable error, and then the number of n's required to obtain that error; 200 seems wildly off scale. And unnecessary: the published data already answers the central question, is the shroud 2000 years old, in a statistically very well documented way: no!
