Understanding and calculating confidence intervals for population proportions - statistics help

This video explains what a confidence interval for a proportion tells us and gives an example of calculation. There are some important aspects to bear in mind at the end of the video.
This is the first video since we gained members, and the first members are named in the credits.

[kbariscelik]

You are amazing. The videos I have watched they were all very helpful. Thank you very much sincerely!

[tomgause]

First, thank you for this video. Question: Before you can calculate a confidence interval, you need to take a sample. How do you know much of a sample to take? In the example you provided, you took 153 (if I recall correctly). Was that a big enough sample to be representative of the entire population for NZ? Do we have to calculate the proper sample size? You said the sample has to be less than 10% of the population. I’m exaggerating here, but if that’s the case, then could I take a sample of 12 or 15 or 20 and still make inferences about the population based on that small of a sample?

[BeastMaker]

Great video.
How is the actual width of the proportion confidence interval calculated?

[bartdude]

The conditions part is a little confusing. So I understand that a larger sample size will create smaller, more narrow confidence intervals because we are sampling a large group of the population. However, you said the condition is that the sample needs to be less than 10% of the population? Why is there a limit to how much we can sample at a time?

[letilovern]

Would it be possible to add closed captioning for this video please? Thank you!

[vinocrichton]

Where did the 0.87 come from when solving the confidence interval?

[rishabhchoudhry]

Why not use t instead of z? (we are using the sample standard deviation and not the population sd). Please help

[ohsintricate]

For my homework I keep getting negative answers. But you can't square root a negative so what am I supposed to What am I doing