DEPARTMENT OF STATISTICS

This study evaluated and compared the performance of three statistical methods for hypothesis testing when comparing means between two populations: the t-test, Welch's t-test, and the z-test. The t-test assumes normally distributed data and equal variances, while Welch's t-test accounts for unequal variances, and the nonparametric Mann- Whitney U test is an alternative for non-normal data. The research aimed to determine the optimal test by formulating hypotheses, selecting appropriate test statistics, determining sample sizes, and implementing the tests using R programming. The data analyzed were the mean heights of NBA guards and forwards during the 2022-2023 season. A power analysis assessed the reliability, validity, and assumptions of the tests. The results indicated a significant difference in mean heights between guards and forwards, with guards being slightly taller on average. Importantly, the Welch's t-test consistently outperformed the standard t-test and z-test across varying sample sizes, demonstrating higher power and a greater ability to detect true effects while minimizing Type I and Type II errors. This superior performance is attributed to the robustness of Welch's t-test in handling unequal variances between groups, a common scenario in real -world data analysis.

This research will undertake a comprehensive statistical analysis of Nigeria's
Exchange rate spanning a decade, with a focus on estimating Autoregressive (AR) models using a prominent statistical methods: the Yule-Walker method. The study aims to provide statistical insights into the underlying dynamics of Nigeria's economic performance during this period. The research will commence by delineating the statistical framework of AR models, which offer a statistical representation of a time series based on its past values. Subsequently, the Yule-Walker method will be introduced, a statistical technique leveraging autocorrelation functions to estimate AR model parameters. The statistical properties of Yule-Walker estimators will be elucidated in the context of Nigeria's Exchange rate data. In contrast, the Least Squares method will be presented as an alternative statistical approach, characterized by its objective to minimize the sum of squared prediction errors. A statistical framework for the least squares estimators will be outlined, providing insights into the statistical properties of parameter estimates and their significance in explaining variations in Nigeria's Exchange rate. The core of the research involves the statistical analysis of Nigeria's Exchange rate time series data over the forty-three year period. The Yule-Walker method will be applied to estimate AR models tailored to the Exchange rate data. The statistical comparison will be based on goodness-of-fit statistics, such as the Akaike Information Criterion (AIC), to evaluate the models' adequacy in capturing the statistical patterns within the Exchange rate dataset.

This study focuses on the development of continuous lifetime distribution to model real life data sets. One approach to creating new distributions is the T-X (Tranformer- Transformed) method, which involves either adding a number of parameters to an existing distribution, raising a distribution to a power or combining existing distributions. In this study, the Paralogistic-Chen distribution is generated using the T-X (Transformer- Transformed) method of obtaining distributions. This involves a combination of the paralogistic and the Chen distributions. Some of the properties of the Paralogistic-Chen distribution are considered in this study and the application of the distribution will be considered to show how well the distribution fits the data and the Maximum Likelihood Estimation (MLE) is used to obtain the parameters of the distribution.

In kernel density estimation, the choice of kernel plays a crucial role in accurately estimating the underlying probability density function. This project focuses on comparing three commonly used kernels: Gaussian, Epanechnikov, and Biweight. The objective is to plot a graph that visually demonstrates the differences between these kernels and evaluate their efficiency using the mean square error metric. First, the theoretical foundations of kernel density estimation are explored, emphasizing the importance of choosing an appropriate kernel. The Gaussian kernel, known for its smoothness and symmetry, is widely used due to its desirable properties. The Epanechnikov kernel, with its compact support and optimal bias-variance trade-off, is another popular choice. Lastly, the Biweight kernel, which balances robustness and efficiency, is considered. To compare these kernels, a graph is plotted to visualize their shapes and characteristics. This graphical representation allows for a clear understanding of how each kernel affects the density estimation. Additionally, the mean square error metric is employed to quantitatively assess the efficiency of each kernel. By calculating the squared differences between the estimated density and the true density, the mean square error provides a measure of accuracy. Through this analysis, valuable insights into the strengths and weaknesses of each kernel can be gained. The graph and mean square error comparisons reveal how the choice of kernel impacts the estimated density function. This information can guide researchers and practitioners in selecting the most suitable kernel for their specific applications. Overall, this project contributes to a deeper understanding of the choice of kernel in kernel density estimation. By focusing on the Gaussian, Epanechnikov, and Biweight kernels, both their graphical representations and efficiency evaluations shed light on their performance in estimating probability density functions.

This study investigates the relationship between JAMB and Post-UTME scores at the University of Benin for the 2021/2022 academic session. Using quantitative methods, it explores the correlation and regression between these scores and their predictive power for academic performance. Reviewing existing literature, the study underscores the importance of considering both scores in admissions. Analysis reveals a positive significant but very low correlation between JAMB and PUTME scores and demonstrates JAMB scores having a weak predictive ability for Post-UTME performance. The study advocates for multi-measure assessment in admissions and concludes with recommendations for future research and policy improvements

This project work conducts a study on graduation of mortality rate using difference equation. The study illustrated the use of difference equation with an example solved manually and with the use of SPSS statistical software. The study started by introducing graduation, smoothness, mortality rates and some measures of mortality. We also looked at the methods of graduation, types of graduation and their advantages and disadvantages. We also looked at the test of graduation, where we considered two test which are the sign test and the chi-square test. Furthermore, the study looked at the meaning of difference equation, and we saw a few examples of difference equation. Methods of solving difference equation were also looked into Finally, illustrations were used to show how graduation of mortality rates works and results showed how we can predict ones death by how old he/she lives using the provided datasets.

In kernel density estimation, the choice of kernel plays a crucial role in accurately
estimating the underlying probability density function. This project focuses on
comparing three commonly used kernels: Gaussian, Epanechnikov, and Biweight. The objective is to plot a graph that visually demonstrates the differences between these kernels and evaluate their efficiency using the mean square error metric. First, the theoretical foundations of kernel density estimation are explored, emphasizing the importance of choosing an appropriate kernel. The Gaussian kernel, known for its smoothness and symmetry, is widely used due to its
desirable properties. The Epanechnikov kernel, with its compact support and
optimal bias-variance trade-off, is another popular choice. Lastly, the Biweight
kernel, which balances robustness and efficiency, is considered. To compare these kernels, a graph is plotted to visualize their shapes and characteristics. This graphical representation allows for a clear understanding of how each kernel affects the density estimation. Additionally, the mean square error metric is employed to quantitatively assess the efficiency of each kernel. By calculating the squared differences between the estimated density and the true density, the mean square error provides a measure of accuracy. Through this analysis, valuable insights into the strengths and weaknesses of each kernel can be gained. The graph and mean square error comparisons reveal how the choice of kernel impacts the estimated density function. This information can guide researchers and practitioners in selecting the most suitable kernel for their specific applications. Overall, this project contributes to a deeper understanding of the choice of kernel in kernel density estimation. By focusing on the Gaussian, Epanechnikov, and Biweight kernels, both their graphical representations and efficiency evaluations shed light on their performance in estimating probability density functions

This study investigates the relationships between economic growth, governmentexpenditure, and interest rates in Nigeria, employing various statistical methods. The research aims to provide actionable insights into the interactions betweenthesecrucial macroeconomic variables and their implications for policymaking. The theoretical foundation draws from Wagner's Law and the KeynesianFramework, which offer contrasting perspectives on whether governmentexpenditure is a cause or effect of economic growth. Using data fromtheCentralBank of Nigeria and the World Bank, the study employs the AugmentedDickey-Fuller (ADF) unit root test to assess stationarity, the Granger causalitytest toexamine causal relationships, and Ordinary Least Squares (OLS) regressiontoanalyze the effects of interest rates and government expenditure onGrossDomestic Product (GDP). The findings confirm the applicability of Wagner's Law in the Nigeriancontext, indicating that economic growth granger-causes government spending. Furthermore, the analysis reveals a positive relationship between interest rates, government expenditure, and GDP, although the results are not statisticallysignificant. The study highlights the importance of interest rates as apolicyinstrument for influencing economic performance and attractingforeigninvestment. To enhance the statistical robustness of the analysis, the study incorporatestheAnalysis of Variance (ANOVA) table, demonstrating its effectivenessin xi evaluating and improving the performance of regression models. The researchculminates in actionable recommendations for policymakers, emphasizingtheneedfor strategic fiscal policies, careful interest rate management, andtargetedinvestments in sectors that foster economic growth. Overall, this study contributes to the understanding of the intricate dynamicsbetween economic growth, government expenditure, and interest rates inNigeria, providing valuable insights for policymakers and researchers alike.