Writing null hypothesis and deciding on rejection criteria

#1
The number of faults in one metre of a thread is Poisson distributed.It is claimed that the average number of faults is 0.02 per metre.A random sample of 100 one metre lengths of the thread reveals a total of 6 faults.Does this information support the claim?

What I want to know whether my H0 should be, H0:lambda=0.02 or should it be lamda=2(0.02*2)

And my next question is in deciding the rejection criteria, Is it enough to check to reject H0,P[X>=6]<0.025 (Testing at 5% significance) or should I have looked for P[X<=6]<0.025 as well and checked whether either one of these is satisfied.

Or calculate 2*P[X>=6] and check if it is less than 0.05