Because populations can be quite large, it is usually impossible to know the exact value of a particular parameter. Parameters could rightly be called "God's Numbers" because, in most instances, only the all-knowing God can know their actual value. Human beings, on the other hand, are stuck with estimates of parameters. A confidence interval is used to estimate a parameter. Usually, you want the width of a confidence interval to be as small as possible because you don't want to look too far for the actual parameter. However, small confidence intervals come at a cost: either you have to have a large sample or reduce your confidence level.

1. Discuss how increasing sample size will decrease the width of a confidence interval. Back up your discussion with illustrative examples that you make up.
2. Discuss how decreasing a confidence level will also decrease the width of a confidence interval. Back up your discussion with illustrative examples that you make up.

Please give detailed answer with calculations where necessary.