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In literature, Lindley distribution is considered as an alternate to the exponential distribution. In the present work, a methodology is developed to discriminate between exponential and Lindley distributions based on the ratio of the maximum likelihoods. Asymptotic distribution of the test statistic under the null hypothesis is derived and the minimum sample size required to discriminate between the two distributions for a user specified probability of correct selection is obtained. Numerical illustrations of the methodology are given through simulated and real life data sets.