Free Statistics Essentials For Dummies by Deborah Rumsey Page A

statistic (for example, a sample mean or proportion.)
     
5. Calculate the margin of error. (Details later in this chapter.)
     
6. Take the statistic plus or minus the margin of error to get your final estimate of the parameter.
     
This is called a confidence interval for that parameter.
     
For example, the formula for a confidence interval for the
mean of a population is ; the statistic here is (the
sample mean), and the margin of error is the piece following
the plus/minus sign: . (This formula is fully broken down
in the section, "Confidence Interval for One Population Mean.")
    The Goal: Small Margin of Error
The ultimate goal when making an estimate using a confidence interval is to have a small margin of error. The narrower the interval, the more precise the results are.
For example, suppose you're trying to estimate the percentage of semi trucks on the interstate between the hours of 12 a.m. and 6 a.m., and you come up with a 95% confidence interval that claims the percentage of semis is 50%, plus or minus 40%. Wow, that narrows it down! (Not.) You've defeated the purpose of trying to come up with a good estimate — the confidence interval is much too wide. You'd rather say something like: A 95% confidence interval for the percentage of semis on the interstate between 12 a.m. and 6 a.m. is 50%, plus or minus 3% (thus between 47% and 53%).
How do you go about ensuring that your confidence interval will be narrow enough? You certainly want to think about this issue before collecting your data; after the data are collected, the width of the confidence interval is set.
Three factors affect the size of the margin of error:
The confidence level
     
The sample size
     
The amount of variability in the population
     
These three factors all play important roles in influencing the width of a confidence interval. In the following sections, you see how.
Note that the sample statistic itself (for example, 50% of vehicles in the sample are semis) isn't related to the width of the confidence interval. The statistic only determines the midpoint of the confidence interval, not its width.
    Choosing a Confidence Level
Variability in sample statistics is measured in standard errors. A standard error is very similar to the standard deviation of a data set or a population. The difference is that a standard error measures the variation among all the possible values of the statistic (for example all the possible sample means) while a standard deviation of a population measures the variation among all possible values within the population itself. (See Chapter 6 for all the information on standard errors.)
The confidence level of a confidence interval corresponds to the percentage of the time your result would be correct if you took numerous random samples. Typical confidence levels are 95% or 99% (many others are also used). The confidence level determines the number of standard errors you add and subtract to get the percentage confidence you want.
When working with means and proportions, if the proper conditions are met, the number of standard errors to be added and subtracted for a given confidence level is based on the standard normal ( Z -) distribution, and is labeled z* . The higher the confidence level, the more standard errors need to be added and subtracted, hence a higher z* -value. For 95% confidence, the  z* -value is 1.96, and for 99% confidence, z* -value is 2.58. Some of the more commonly used confidence levels, along with their corresponding z* -values, are given in Table 7-1.

Using stat notation, you can write a confidence level as (1 - ), where represents the percentage of confidence intervals that are incorrect (don't contain the population parameter by random chance). So if you want a 95 percent confidence interval, = 0.05. This number is also related to the chance of making a Type I error in a hypothesis test (see Chapter 8).
    Factoring In the Sample Size
The relationship between margin of error and sample size is