A biologist is studying the effects that applying insecticide to a fruit farm has on the local bat population. She collects 23 bats and finds the mean weight of this sample to be 503.4 grams. Assuming the selected bats are a random sample, she concludes that because the sample mean is an unbiased estimator of the population mean, the mean weight of bats in the population is also 503.4 grams. Explain why this is an incorrect interpretation of an unbiased estimator.

In Statistics,if the sample mean is an unbiased estimator of population mean,then the expected value of the sample mean is equal or identical to the actual population mean.
As the researcher increases the size of the random sample in any statistical study or research, the sample mean increasingly approaches the actual population mean and hence, with increasing sample size with relation to the actual population of the study,the sample mean will become an unbiased estimator of the population mean.
In this instance, the biologist has selected only 23 bats for the concerned study which might not be enough considering the entire or actual local bat population. Therefore, even a random sampling of 23 bats will not necessarily ensure that the sample mean will be an unbiased estimator of the population mean, in this case. Hence, the biologist would have to increase the size of the random sample to establish the unbiasedness of the sample estimate or the mean.