DEPARTMENT OF STATISTICS

The research work explores the comparison of various methods for estimating variance components in a two-way random effects model, a critical task in experimental data analysis. The methods assessed include classical Analysis of Variance (ANOVA), Restricted Maximum Likelihood (REML), and Bayesian estimation. The experiment was designed with treatments (3 levels) and blocks (4 levels), with each combination replicated 5 times, resulting in 60 observations. The objective was to estimate variance components attributable to treatments, blocks, and errors. The results were compared across the three methods: ANOVA produced variance components of σ²α = 3.84, σ²β = 2.43, and σ²ε = 3.58, while REML and Bayesian estimates were σ²α = 4.805 and 4.75, σ²β = 2.4067 and 2.60, and σ²ε = 3.58 and 3.60, respectively. While the three methods yielded similar results, minor differences were observed, reflecting their respective properties. ANOVA, though simple and interpretable, may be biased in small samples or unbalanced designs, whereas REML offers better performance in such situations, and Bayesian estimation provides flexibility with credible intervals to quantify uncertainty. The research work highlights the importance of method selection depending on sample size, design, and the need for uncertainty quantification, suggesting future work on more complex or larger-scale experiments.

The work is intended to study the moments of distributions and in particular pareto-II distribution named after Italian scientist, Vilfred pareto. This study was guided by the following objectives; to obtain the rth moment, obtain the mean, variance, skewness and kurtosis of the pareto-II distribution and finally obtain some numerical results of the moment. The study employed the knowledge of differential and integral calculus with transformation of variables to obtain several expressions as we shall be seeing. Statistical software "R" was used to run analysis and obtain numerical results of the moments. Finding revealed that the parameters of the distribution are important in determining the behavior of the moments. From the findings, it implied that the study of moments is important and applicable to study of distributions. Keywords Moments, Parameter, Distribution, Mean, variance, skewness, kurtosis.

Understanding customer’s preference for product features is crucial for businesses seeking to optimize their offerings and increase sales. This study aims to identify key product features that significantly influence purchasing decisions. The researchspecifically examines customer preference across different demographic groups, such as age and income levels, to determine variations in product feature importance. Using chi-square test for analysis, this study evaluates the association between demgraphic factors and product features preferences, providing insight into customer’s decision-making patterns. Based on the analysis it was found that the key product features that affect customers purchasing decision is quality and performance. The findings will help businesses tailor their marketing and product development strategies to better align with costumer expectations.

This research undertakes a comprehensive statistical analysis of Nigeria's Gross Domestic Product (GDP) spanning a decade, with a focus on estimating Autoregressive (AR) models using two prominent statistical methods: the Yule-Walker method and the Least Squares method. The study aims to provide statistical insights into the underlying dynamics of Nigeria's economic performance during this period. The research commences by delineating the statistical framework of ARmodels, which offer a statistical representation of a time series based on its past values. Subsequently, the Yule-Walker method is introduced, a statistical technique leveraging autocorrelation functions to estimate AR model parameters. The statistical properties of Yule-Walker estimators are elucidated in the context of Nigeria's GDP data. In contrast, the Least Squares method is 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 is outlined, providing insights into the statistical properties of parameter estimates and their significance in explaining variations in Nigeria's GDP. The core of the research involves the statistical analysis of Nigeria's GDP time series data over the 10-year period. Both the Yule-Walker and Least Squares methods are applied to estimate AR models tailored to the GDP data. The statistical comparison is 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 GDP dataset.

his study looks into the spending behavior of students at the University of Benin, Nigeria, in order to establish the relationship between demographic factors such as gender, age, and academic level on expenditure behaviour. The purpose of the study was to gain a better understanding of how students’ money is spent in areas of food, transport, housing, academic materials, and personal expenses. A quantitative approach was used in the study where 228 questionnaires were completed and descriptive and inferential analysis were employed on the data collected. The results show that the amount of money spent by the students on food, transport, and housing is highest. The results of the statistical analysis indicate that there is no significant association between the gender of the respondent and the primary source of income, however, more males are likely to save than females. The result of the study shows that the academic level affects the spending and higher-level students spend more money on the necessities. The transport expense also depends on the age of students, the older students spend more money on transport.
The results conclude that, among students, academic level and age are important predictors of spending behaviour; the impact of gender is limited to saving behaviour. For practice, it is suggested that financial literacy be enhanced, housing and transportation be made cheaper, and financial aid be increased. Further research could be directed towards the patterns of spending at different universities, changes over time, the effect of financial aid and part-time employment on spending. This research can help to explain student financial problems and offers some practical suggestions for students, administrators and policymakers.

This study examines the influence of Artificial intelligence on jobs: unemployment and displacement. It captures the implication of Artificial intelligence on the workforce as a whole. The Literature review of the study was segmented into three(3) sections namely; Conceptual review, Theoretical review, and Empirical review. Major Statistical tools of analysis used includes; data visualizations using histograms and the multinomial logistic regression. All tests done were conducted at the 0.05 level of significance. Major findings show that python, AI algorithms, certifications, problem solving, mathematics, and the other skills have a significant effect on getting an AI-related job. The study concludes that the impact AI has on jobs, is more on job loss as regards low-skilled workers, however AI has the ability to complement human workers, which will in turn lead o increased efficiency and productivity. Also as regards job displacement, it will affect mainly low-skilled and routine jobs.

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.