Final answer:
The maximum likelihood estimator is a biased estimator of the error variance especially in small samples since it doesn't compensate for degrees of freedom used in estimating other parameters. The sample variance is an unbiased estimator as it corrects for this usage of degrees of freedom.
Therefore, option 4) is correct.
Step-by-step explanation:
An example of a biased estimator of the error variance is the maximum likelihood estimator (option 4). The maximum likelihood estimator is often biased for variance parameters in finite samples. In the context of simple linear regression, the error variance (true variance of the errors) can be underestimated by the maximum likelihood estimator, particularly when the sample size is small. This is because the maximum likelihood estimator doesn't adjust for the degrees of freedom lost by estimating other parameters like the mean.
In comparison, the sample variance (option 2) is an unbiased estimator of error variance when the sample mean is used to estimate the population mean and is calculated by dividing the sum of the squared deviations from the sample mean by n-1, where n is the sample size. The factor of n-1 corrects for the bias introduced by using the sample mean rather than the true population mean.