A simple method of finding a biased estimate of the population proportion is introduced. This biased estimate is derived by finding a confidence interval for the population proportion without using the concept of convergence in probability. While all existing biased estimates of the population proportion are based on specific prior distributions, the biased estimate discussed here does not require any prior distribution. The proposed biased estimate is asymptotically unbiased, has smaller variance and smaller maximum mean squared error than the sample proportion. Under certain conditions it also has a smaller margin of error and smaller mean squared error than the sample proportion.