Estimation: Point and Interval Estimates

Estimation is the process of using a sample statistic to infer the value of an unknown population parameter. There are two kinds of estimates:

• A point estimate is a single number used as the best guess for the parameter — e.g., using the sample mean $\bar{x}$ as the estimate of the population mean $\mu$. A point estimate is simple, but it gives no idea of how close it is likely to be to the true value.
• An interval estimate (or confidence interval) gives a range of values, together with a stated level of confidence, within which the true population parameter is expected to lie. This is almost always more useful in business decisions, because it conveys the precision of the estimate along with the estimate itself.

For a large sample, a confidence interval for the population mean $\mu$ is built around the sample mean $\bar{x}$ using the standard error and a value $Z_{\alpha/2}$ from the standard normal table corresponding to the desired confidence level:

The most commonly used confidence levels and their $Z_{\alpha/2}$ values are: