1. Why 95? You've probably noticed that most of the confidence intervals we've considered have been at the 0.95 level, and also that we always seem to use at least 90%, but never more than 99%, confidence. There is actually a mathematical explanation for this. Calculate the margin of error associated with estimating the mean of a normal population (Section 7.2) for a series of confidence levels (Start at around 80% and increase in half percent increments to 99.5%). Draw a graph of margin of error as a function of confidence level. Use your results to defend the predominant use of 95% confidence, and also why confidence levels less than 90% or greater than 99% are seldom used.

2. How big? We saw that the margin of error and related sample size formula (7.6-2) for estimating a population proportion is still valid in practice when sampling without replacement, as long as the population size (N) is large relative to the sample size (n) (we might say the population is "essentially infinite" in this case). Otherwise, the formulas on p.391 are appropriate. However, we did not specify what exactly what we meant by "large". Assume we will sample without replacement to try to estimate the proportion of a finite population in favor of a certain issue, and wish to have 95% confidence our estimate is within 3% of the true proportion in favor. How big must the population be before we can consider it "essentially infinite"? Justify your answer. Assume for the purposes of this assignment that the population is evenly split on this issue, i.e. that 50% are in favor and 50% are not.