In this study, we developed an inference procedure for the neural network using the bootstrap approach, and applied it to the market efficiency of the Nigerian exchange rate. Data used are exchange rate values from 2001 to 2015. We conducted a test on the market efficiency hypothesis, including test for relevance of individual and joint network inputs using method of partial derivative. The network architecture used is the multilayer perceptron. A valid statistical inference based on the estimated Statistical Neural Network was conducted using a well-known statistical resampling technique. Test of hypothesis that input or groups of inputs are relevant to a model was carried out at 1% and 5% levels of significance. Evaluation of model was carried out using the Durbin Watson and Ljung-Box tests (the test statistic are obtained are 1.98 and 0.5831 respectively). The tests showed that the residuals were independently and identically distributed and had no serial autocorrelation in the series. The exchange rates do appear to contain information that is exploitable for enhanced point prediction. Hence, the Implication of this is that there are possibilities of abnormal earning for the agents in this market.