Robustness of Inference for One-sample Problem with Correlated Observations

The inference about the population mean based on the standard t-test involves the assumption of normal population as well as independence of the observations. In this paper we examine the robustness of the inference in the presence of correlations among the observations. We consider the simplest correlation structure AR(1) and its impact on the t-test. A modification of the t-test suitable for this structure is suggested, and its effect on the inference is investigated using Monte Carlo simulation.