hypothesis testing question

ii) is similar to i) but the "no members receive" is one of the extreme values of the binomial distribution with a simple joint probability.

so I think I might have to try work out p(0) from B(n,0.35) but I'm not sure how to do that without knowing what n is. could I do 0.65^n is larger than 0.025

Yes (bold). They're trying to see if you understand what hypothesis testing represents for a slightly different scenario, rather than punching numbers into your calc.

thank you. obviously for this scenario it was easier as when I put it into the binomial distribution formula, n choose zero equalled one and 0.35 ^0 =1. But if this was not the case and I was asked to find for e.g. P(2), is there another method I could take for all situations?

Not sure I fully understand what youre asking, but this question "works" (simple expression) because the cumulative distribution is just the joint 0.65^n and can be solved using logs. More generally, if the cumulative involved 0, 1, 2 households (for instance), that would be the sum of 3 expressions involving n as powers (0.65^n, 0.35^n) and multipliers (nCr). As its the sum of expressions of n, there is no simple closed form solution based on logs.

sorry for my lack of clarity, I understand what you are saying. However I just found the mark scheme online and it seems that they had another method of finding the value out without using logs. Just wondering if this other method they used (which I can't decipher from the ms) can be applied to more ranges of situations

Looks like their other "method" is to punch values for n into your calculation until two bracket 0.025. Its a valid solutio though monkeys and typewriters comes to mind ... The previous post stands, there isn't a simple closed form expression in general.
The standard way to evaluate the cumulative binomial is using your calculator and you can obviously do this for different values of n as long as you don't get bored.