ABSTRACT
Confidence intervals can be computed for many different population parameters by using the standard error of the statistic and the confidence level. The standard error of a statistic was described in the previous chapter, e.g., standard error of the mean. The variance of a sampling distribution indicates the amount of error in estimating the population parameter. Smaller sampling variance reflects less error in estimating the population parameter. The standard error of a statistic is computed as the standard deviation of the sampling distribution divided by the square root of the sample size. Consequently, as sample size increases, the standard error of the statistic decreases. A confidence interval is computed using the sample statistic and the standard error of the statistic (standard deviation of the statistic in the sampling distribution). The confidence interval around the sample statistic is a range of values that should contain the population parameter. A confidence level is used which defines how confident we are that the interval around the sample statistic contains the parameter being estimated. The confidence interval is determined by picking an area in the tail of the sampling distribution in which the value of the statistic is improbable. Recall that a sampling distribution is a frequency distribution; therefore we could pick a 5% probability area, leaving 95% of the sample statistics in the frequency distribution as plausible estimates of the population parameter.
