In the present study, approximate Bayesian confidence intervals for the variance of a normal population under two different loss functions have been derived. The loss functions that are employed are the square error and the Higgins-Tsokos loss functions. Based on the above numerical results we can conclude the following: The classical method used to construct confidence intervals for the variance of a normal population does not always yield the
best coverage accuracy. In fact, each of the obtained approximate Bayesian confidence intervals contains the population variance and is strictly included in the corresponding confidence interval obtained with the classical method. Contrary to the classical method that uses the Chi-square statistic, the proposed approach relies only on the observations. With the proposed approach, approximate Bayesian confidence intervals for a normal population variance are easily computed for any level of significance. The approximate Bayesian approach under to the popular square error loss function does not always yield the best approximate Bayesian results. In fact, the Higgins-Tsokos loss function performs better in the above examples. Bayesian analysis contributes to reinforcing well-known statistical theories such as the estimation theory.