Relation between confidence interval, confidence level, and sample size

[bsaikrishna]

Hi

I am penning down my theoretical understanding of confidence interval, confidence level, and sample size. Kindly let me know if this is correct and truly applies in practice or not.

I have taken a sample of size 1000 ( out of a population of 0.2 million, assume sample is representative). I have asked all these people the likeability of a brand of beer on a scale of 1 to 10.

Assume the mean score is 6.4 out of 10
Assume Confidence Interval: 95%, and confidence level: 95%
The 95% confidence interval is: 5.9 to 7

Now, I can say the statement: I am 95% confident (confidence level) that the population mean likeability is in the range of 5.9 to 7 (confidence interval).

What happens if I want to decrease the confidence level to 80%? How exactly is the confidence level determined? How do I know which confidence level is good for a particular problem or set of data?

[bsaikrishna]

I got the answer: As we are reducing the confidence level to 80%, logically we can narrow the confidence interval.

But, how does the relationship actually work?

So, to decrease my confidence interval either I can increase my sample size or decrease my confidence level.