S2 help, hypothesis testing

I looked at the solution to this question, and they use 0.5 as their probability of success. And I can't understand how they got this. As I used, 4/5, 0.8, which is wrong apparently.

Can someone please show me how they worked out 'p' to be 0.5?

should it not be distributed like this X~B(5,0.8)?
solution uses X~B(5,0.5)

Thank you, in advance.

You don't mention a significance level.

It says in the caption that it needs to be tested at a significance level of 5%.

Thanks I understand it now, however I don't get why you would use 0.5, why not any other number?

Can you please explain why you would assume that the probability of people liking/disliking supergold is 0.5?

hope this makes sense,
thanks.

rnd puts it quite nicely 'The null hypothesis would be (that) there is no preference for either.'

I'm sure you've covered the null hypothesis. When you are doing these significance tests, you start with a standard distribution that you predict it will follow. You'd expect that if you tossed a fair coin n number of times that the probability of landing heads (success) is equal to landing a tails (fail). We designate heads as success and tails as fail here. Now if someone claimed that the coin was unfair, and the coin was tested and the results showed that 9/10 times the coin landed heads. We look at the probability that $P(X \geq 9)$. So in this case we start with p = 0.5, that the coin is equal and test claims that it is not.

Thanks, I get what your saying, but with the coin example you 'already' know the likely probability of getting a head or a tail, therefore you can predict a null hypothesis. You know that a normal unbiased coin is 50/50 heads or tail. Where as with this example we assumed?

You see where I am getting confused?

appreciate your help,
thanks