This paper analyzes the accuracy with which the drug-resistant sub-population of cancer cells in a tumor can be estimated from measurements of total tumor size. The paper is motivated by two key facts. First, drug resistance is one of the main reasons for the failure of cancer chemotherapy treatment: a fact that makes it critical to monitor and estimate such resistance. Second, recent research has shown that above a threshold level of drug resistance, the optimal treatment protocol is one that regulates total cancer size rather than attempting to eliminate the cancer. This makes the accurate estimation of resistance critical for treatment protocol selection. The literature already examines the causes and dynamics of resistance in cancerous tumors. However, the problem of determining the accuracy with which the prevalence of resistance can be estimated remains relatively unexplored. To address this gap in the literature, we apply Fisher information analysis to the problem of estimating the fraction of a total cancer cell population that is drug-resistant, assuming a constant drug administration rate. Our analysis reveals that drug-resistant cell population estimation accuracy worsens with increasing drug administration rate up to the point where the drug-sensitive and drug-resistant cell population growth rates are equal. Beyond that point, additional drug administration improves resistance estimation accuracy.