Stats Help Please?

Question

True or False
As you increase the confidence level (everything else remaining the same), the width of the confidence interval increases.

AND

As you increase n(assuming everything else remains the same), the width of the confidence interval increases.

Answer 1

The confidence level determines how often a particular sample average will fall inside the confidence interval. So let's look at extremes, shall we? If you have a confidence level of 100%, any sample you take MUST lie in the interval. How can you be sure it's going to fall in the interval? You make the interval huge. So, all things being the same, a high confidence level means a large confidence interval. The first statement is true.

Now n is the size of the sample you're going to take. Like rolling dice, the more you roll, the more your results should be in line with the calculated average result. If, hypothetically, your n was equal to ALL your samples, then you'd get the same average every time, and you wouldn't need an interval at all! So, all things being the same, the bigger your n, the smaller an interval your'e going to need. The second statement is false.

Hope that helps!

Answer 2

I know the first part of the answer is true. Like in a bell curve, to get from 2/3 accuracy to 99% accuracy, you have to go from a confidence level of 1 width to 3 width. The second part, I'm not totally sure on. It seems like the longer the period of time, it could be that you have more data and it is more accurate. But it could be that the longer the period of time elapsed, the less confident you would be since you don't know what's going to happen years in the future. Hope someone else can clarify better. Good luck

Answer 3

This site is very helpful
http://www.math.com