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After the scientific problem of interest is defined, collecting data is the first stage of any statistical analyses. The question of how large the sample should be is thus of great interest. In this thesis we demonstrate that in a geostatistical experiment determining the minimum sample size to achieve a certain precision of an estimator is often not possible due to inconsistencies of the estimators. This thesis is an empirical work extended from a manuscript (Gombay, 2010), which shows that the laws of large numbers may not hold under the spatial setting. It is demonstrated by a simulation study that the variance of the kriged mean converges to a non-zero constant as the sample size keeps increasing. It then followed by further investigations on the simple and ordinary kriging estimators. The conclusions arrived in this thesis lead for further research on the topic.