Now, let's have a look how big the confidence interval is. Remember, the formula for the interval is we take the estimate plus/minus z times standard error. So the width of the confidence interval is given by twice z times standard error. That term, z times standard error, is called the margin of error. So remember, the square-root law says that the standard error is given by sigma over square-root n. And what that means is that the width goes down as the sample size n increases. However, because there's a square-root there, that means that if we want to cut the width in half, we need four times the sample size. And likewise, if we wanted one-tenth of the width, we would need 100 times the sample size. Another option to make the confidence interval smaller is to make z smaller. Remember, z is determined by the confidence level. So we can make z smaller by choosing a smaller confidence level. For example, instead of using a confidence level of 95%, we could use 80%. So there's a trade off here. We would get a smaller confidence interval at the cost of having less confidence that it covers the true parameter mu. If we're interested in confidence intervals for percentages, then there's a simple rule of thumb that allows us to compute its confidence intervals on the fly. The rule of thumb says, just take the estimated percentage plus/minus 1 over square root sample size. The reason why this works is because sigma can be shown to be never larger than one-half no matter what the population parameter p is. So, if we plug this into our formula for the standard error, we see that z times standard error, where z equals 2 and sigma is not more than a half, and those 2s cancel out, and so, we are left over with that rule of thumb. Sometimes, newspaper articles give confidence intervals without stating a confidence level. In that case, it's tacitly assumed that the confidence level is 95%.