Basically it involves looking at the resuts from a sample (i.e. number of corpuscles =8) and deciding how likely it is that those results (or worse results i.e. >8) could have occurred under the null hypothesis (i.e. mean = 3.5). If the probability of the sample results occurring under the null hypothesis is deemed too low (i.e. under 5%), the null hypothesis is rejected and the alternative hypothesis is accepted.
So, null hypothesis: λ = 3.5
alternative hypothesis: λ > 3.5
If null hyp. is true:
So, P(X>=8) = 0.0099
Since 0.0099<0.05, this is treated as significant and the nulll hypothesis is rejected. Therefore, there is sufficient evidence to suggest that the mean has increased.
Sorry if i haven't explained this very well.