Oshome, Caren Miriel2025-02-212025-02-212024-11https://ir-library.ku.ac.ke/handle/123456789/29618A Research Project Submitted in Partial Fulfilment of the Requirements for the Award of the Degree of Master of Science (Statistics) in the School of Pure and Applied Sciences of Kenyatta University, November 2024.Estimation of population parameters such as population mean and population total has been a major concern in Sample Survey Theory. In sampling theory, Authors employ auxiliary information to improve precision and validity of estimators. This study applies two-phase sampling in estimation of a finite population mean using modified exponential ratio estimator. Two-phase sampling was used since it leverages on the information collected in the first phase, along with auxiliary variables, to guide the selection of a more targeted and efficient second-phase sample, resulting in increased precision for the estimates of interest. Study results showed that the proposed modified exponential ratio estimator produced a smaller Bias and MSE than Shabbir and Gupta (2007), and Singh and Solanki (2013). Further, the proposed estimator produced a higher relative efficiency as compared to Shabbir and Gupta (2007), and Singh and Solanki (2013).enThesis