Point Estimators for Different Situations

As we have seen before, we have several natural point estimates for the various situations we will consider:

1. For one sample from a continuous population, we use to estimate and to estimate .
2. For independent samples from continuous populations, we use to estimate the difference and to estimate . If we know that the variances of the two populations are the same, that is, , say, then we use the pooled estimate of variance,

   

   to estimate .

3. For paired data, we use the mean, , and variance, of the n differences in the pairs to estimate the mean and variance of the population of differences.
4. For one sample from a 0-1 population we use the sample proportion p to estimate the population proportion , while for two independent samples we use to estimate .
5. In the correlation setting, we use the sample correlation coefficient r to estimate the population correlation coefficient and the slope and the intercept of the least squares line to estimate the slope and intercept of the true population line.