3.1 Point Estimate

If we have to name one value for the population value, our best guess is the value of the sample statistic. For example, if 18% of the candies in our sample bag are yellow, our best guess for the proportion of yellow candies in the population of all candies from which this bag was filled, is .18. What other number can we give if we only have our sample? This type of guess is called a point estimate and we use it a lot.

The sample statistic is the best estimate of the population value only if the sample statistic is an unbiased estimator of the population value. As we have learned in Section 1.2.5, the true population value is equal to the mean of the sampling distribution for an unbiased estimator. The mean of the sampling distribution is the expected value for the sample.

In other words, an unbiased estimator neither systematically overestimates the population value, nor does it systematically underestimate the population value. With an unbiased estimator, then, there is no reason to prefer a value higher or lower than the sample value as our estimate of the population value.

Even though the value of the statistic in the sample is our best guess, it is very unlikely that our sample statistic is exactly equal to the population value (parameter). The recurrent theme in our discussion of random samples is that a random sample differs from the population because of chance during the sampling process. The precise population value is highly unlikely to actually appear in our sample.

The sample statistic value is our best point estimate but it is nearly certain to be wrong. It may be slightly or far off the mark but it will hardly ever be spot on. For this reason, it is better to estimate a range within which the population value falls. Let us turn to this in the next section.