Chapter 9.4, Problem 35MS

Even more confident. Mindscape 27 gives a more accurate formula $\text{(than 1/}\sqrt{\text{n}}\text{)}$ for the margin of error corresponding to a sample size of n trials as follows. If p equals the probability of success by randomness alone on each trial, then the margin of error for a 95% confidence interval is $\text{1}\text{.96}\times \sqrt{p\times (1-p)/n.}$. Suppose $p=0.4$ and $n=200$. Find the more accurate value for the margin of error associated with a 95% confidence interval.