Week 4 Discussion - Confidence Interval

A point estimation is a sample statistic that gives a good guess about a population parameter. In the same way, a point estimate of the mean overpayment is simply a good guess about what the average overpayment for the population is. Investigating all 1,000 claims and obtaining the overpayment amount for each would either be impractical, unfeasible or both. Thus, the auditor deems a sample size of 50 claims to be adequate and sufficiently representative of the entire population. The mean overpayment amount of this sample is then calculated in order to obtain a point estimate of the mean overpayment. The estimated mean is then extrapolated to the overpayment amount to the population of all 1,000 claims.

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Point Estimate vs. Interval Estimate
To estimate population parameters, statisticians use sample statistics. For example, we use sample means to estimate population means and we use sample proportions to estimate population proportions.
An estimate of a population parameter can be expressed in one of two ways: * Point estimate. A point estimate of a population parameter is a single value of a statistic. For example, the sample mean x is a point estimate of the population mean μ. In the same way, a sample proportion p is a point estimate of the population proportion P. * Interval estimate. An interval estimate is defined by two numbers, and the population parameter is said to lie between those two numbers. For example, a < x < b represents an interval estimate of the population mean μ. It expresses that the population mean is greater than a but less than b.
Confidence Intervals
To express the precision and uncertainty that are associated with a particular sampling method statisticians use a confidence interval. A confidence interval consists of three parts: * A confidence level. * A statistic. * A margin of error.
The confidence level is used to describe the uncertainty of a sampling