Abstract : <p>A common technique employed in medical research is to answer questions using statistical inference and to calculate an appropriate test statistic and confidence interval that will determine whether some hypothesis should be rejected or otherwise. There are many issues to consider, including the controversial matter of whether a one- or two-sided alternative is appropriate. The objective of this paper is to provide a precise interpretation of a confidence interval as well examining how conditional probability should be interpreted. A novel approach is undertaken for explaining the p-value in relation to a confidence interval that has been used to test a medical hypothesis. It is also apparent that even skilled medical researchers have not been sufficiently trained in statistical analysis do not have the ability to interpret statistical results. Examples to illustrate the techniques are provided. The results in this paper will enable the medial researcher to better understand the nature of confidence intervals and to use them more effectively in reaching conclusions. It is known that there are a number of medical research articles appearing in refereed journals that contain erroneous conclusions through the misinterpretation of data analysis. This paper uses a case study to illustrate that their findings can often be misleading or just plain wrong.</p>