Inferential statistics -3,4

This comprehensive, well-structured set of handwritten notes covers Modules 3 and 4 of Statistics and Information Systems, specifically designed for university exam preparation. Module 3 focuses on parametric testing, detailing the foundational concepts of setting up null ($H_0$) versus alternative ($H_1$) hypotheses, distinguishing between one-tailed and two-tailed tests, and identifying critical regions on sampling distribution curves. It provides step-by-step procedures and clear mathematical formulas for calculating Type I ($\alpha$) errors, Type II ($\beta$) errors, and the overall power of a test ($1-\beta$). Students will find fully solved engineering and classroom problems for large-sample Z-tests, small-sample Student's t-tests (with degrees of freedom), and methods to evaluate the significant differences between two population means. Module 4 transitions into non-parametric inference, beginning with conditional probability applications using contingency tables. It features deep dives into the Chi-Square ($\chi^2$) test as a metric for goodness of fit and a test of independence among multiple attributes. Additionally, the notes layout practical formulas for the F-test to check the equality of population variances alongside complete, structured computational steps for both One-Way and Two-Way Analysis of Variance (ANOVA) tables. Packed with formula blocks, summary steps, and past exam questions that conclude with definite acceptance or rejection decisions, this material serves as an efficient study aid for assignments, quick revisions, and viva preparation.