Moment measures are widely used to describe the properties of samples. The third and fourth moment, descriptors of skewness and kurtosis, may be used to test the hypothesis that the sample came from a normal distribution. This paper uses a Monte Carlo method to devise tables for this purpose. The approach involves repeated sampling from a normal population to determine the percentage points of the distribution of the estimators of skewness and kurtosis. The tables are arranged to indicate the limiting values of skewness and kurtosis that are acceptable without rejecting the hypothesis that the population is normal.