As an example, consider determining whether a suitcase contains some radioactive material. Placed under a Geiger counter , it produces 10 counts per minute. The null hypothesis is that no radioactive material is in the suitcase and that all measured counts are due to ambient radioactivity typical of the surrounding air and harmless objects. We can then calculate how likely it is that we would observe 10 counts per minute if the null hypothesis were true. If the null hypothesis predicts (say) on average 9 counts per minute, then according to the Poisson distribution typical for radioactive decay there is about 41% chance of recording 10 or more counts. Thus we can say that the suitcase is compatible with the null hypothesis (this does not guarantee that there is no radioactive material, just that we don't have enough evidence to suggest there is). On the other hand, if the null hypothesis predicts 3 counts per minute (for which the Poisson distribution predicts only % chance of recording 10 or more counts) then the suitcase is not compatible with the null hypothesis, and there are likely other factors responsible to produce the measurements.

In order to be certain of showing that it was a matter of new elements, the Curies would have to produce them in demonstrable amounts, determine their atomic weight and preferably isolate them. To do so, the Curies would need tons of the costly pitchblende. However, it was known that at the Joachimsthal mine in Bohemia large slag-heaps had been left in the surrounding forests. Marie considered that radium ought to be left in the residue. A sample was sent to them from Bohemia and the slag was found to be even more active than the original mineral. Several tons of pitchblende was later put at their disposal through the good offices of the Austrian Academy of Sciences.

In 1897, her daughter Irène was born. To support her family, Curie began teaching at the École Normale Supérieure . [22] The Curies did not have a dedicated laboratory; most of their research was carried out in a converted shed next to the School of Physics and Chemistry. [22] The shed, formerly a medical school dissecting room, was poorly ventilated and not even waterproof. [29] They were unaware of the deleterious effects of radiation exposure attendant on their continued unprotected work with radioactive substances. The School did not sponsor her research, but she would receive subsidies from metallurgical and mining companies and from various organizations and governments. [22] [29] [30]