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Often, the most practical way to decrease the margin of error is to increase the sample size. Usually, the more observations that you have, the narrower the interval around the sample statistic is. Thus, you can often collect more data to obtain a more precise estimate of a population parameter.
You should weigh the benefits of increased precision with the additional time and resources required to collect a larger sample. For example, a confidence interval that is narrow enough to contain only the population parameter requires that you measure every subject in the population. Obviously, such a strategy would usually be highly impractical.
The less that your data varies, the more precisely you can estimate a population parameter.
That's because reducing the variability of your data decreases the standard deviation and, thus, the margin of error for the estimate. Although it can be difficult to reduce variability in your data, you can sometimes do so by adjusting how you collect data. For example, you can use a paired design to compare two groups. You may also be able to reduce variability by improving the process so that the process is more consistent or by measuring more precisely.
A one-sided confidence interval has a smaller margin of error than a two-sided confidence interval. However, a one-sided interval indicates only whether a parameter is either less than or greater than a cut-off value. A one-sided interval does not provide any information about the parameter in the opposite direction. Thus, use a one-sided confidence interval to increase the precision of an estimate only when you are worried about the estimate being either greater or less than a cut-off value, but not both.
For example, a beverage company wants to determine that the amount of dissolved solids in their drinking water. The fewer dissolved solids they have, the better. When they calculate a two-sided confidence interval, the upper side of the interval is 18.4. However, because the company only cares about the upper bound, they can calculate a one-sided confidence interval instead. The one-sided confidence interval shows that the upper bound for the amount of dissolved solids is even lower, 17.8 mg/L.
The advantage of a lower confidence level is that you get a narrower, more precise confidence interval. The disadvantage is that you have less confidence that the confidence interval contains the population parameter you are interested in.
So lower the confidence level only if, in your situation, the advantage of more precision is greater than the disadvantage of less confidence. For example, if it's too expensive to increase the sample size in your study, lowering the confidence level will shorten the length of the interval at the expense of losing some confidence.
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