OCR S3 June 08 q6ii help (Confidence Intervals)

Firstly, sorry if this is in the wrong forum, given that just over 300 people take this exam in a year, I'll be surprised if I even get an answer. My textbook has nothing on this sort of question and my teacher deliberately avoided the theory. Googling also provides little help (...most of the results are about the Scottish Government, Confidence Intervals are a weird topic to Google).

See attached for the question and mark scheme. Part (i) I can do just fine (but I have no idea what they mean by "limits"), (ii) is where I have my issue.

The method they've used keep the proportions as they were in part (i) but increases the sample size. How is this a valid move? Surely if they've increased the sample size, then they must be considering a new sample, and therefore the proportions are highly unlikely to match what they were in part (i).

Can anyone explain this? The best I've got so far was from the report on the exam "Those who had seen similar had little difficulty with this part.", though personally I'd like to know where anyone's seem similar to this .

Thanks for any help, also as a side question, given how few people sit S3, will I have an easier time doing the mandatory stats module at uni than most other people? (the one usually titled "Probability and Statistics" that all Maths undergrads seem to have to take in their first year) I kinda like the idea that in my year at uni, I might start out as the most knowledgable of stats.