One important characteristic in choosing a sample statistic as a point estimate of the value of the population parameter is that the sample statistic be an unbiased estimator. An estimator is unbiased if the expected value of the sample statistic is identical to the population parameter it is supposed to estimate. Each of the several sample statistics we have looked at this term are unbiased estimators of their population counterparts. Finally, p, the sample proportion is an unbiased estimator of , the population proportion. An interval estimate is a range of values within which the actual value of the population parameter may fall.
Interval limits are the lower and upper values of the interval estimate.
Accuracy is the difference between the observed sample statistic and the actual value of the population parameter being estimated. This may also be referred to as estimation error or sampling error. When using this equation, one assumes that the underlying population is normally distributed or that the sample size is and normality is achieved through the central limit theorem. It was discovered that when the population standard deviation was unknown, and particularly when the sample size was small, that the normal distribution was not exactly appropriate to provide accurate confidence statements for estimating population means with sample estimates. Because his work on this difficult problem was very important and gave the Guiness Brewery a significant market advantage, Gosset was not allowed to publish his findings.