DTS 2243 units200 LevelSecond Semester

Statistical Inference and Modelling

B.Sc. Data Science, University of Uyo

Reasoning from a sample to a population: estimation, confidence intervals, hypothesis testing, and the linear model. The core statistical machinery of the degree — and the part most often misused in practice.

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Course outline

  1. 01Populations, samples, parameters and statistics; sampling distributions
  2. 02The Central Limit Theorem and its practical consequences
  3. 03Point estimation: unbiasedness, efficiency, consistency; method of moments and maximum likelihood
  4. 04Interval estimation: confidence intervals for means, proportions and variances
  5. 05Hypothesis testing: null and alternative hypotheses, test statistics, p-values, Type I and Type II errors, power
  6. 06One- and two-sample tests: z, t, chi-square and F tests
  7. 07Analysis of variance (ANOVA): one-way and two-way
  8. 08Simple and multiple linear regression: estimation, interpretation, inference on coefficients
  9. 09Model diagnostics: residual analysis, multicollinearity, and the assumptions of the linear model

Recommended textbooks

  • Mathematical Statistics with Applications — Wackerly, Mendenhall & Scheaffer

    7th ed. — rigorous and complete

  • Statistical Inference — George Casella & Roger L. Berger

    2nd ed. — the graduate-level reference; consult rather than read cover to cover

  • OpenIntro Statistics — Diez, Çetinkaya-Rundel & Barr

    4th ed. — free; the best explanations of p-values and confidence intervals

How to pass DTS 224

  • Learn what a p-value actually is and — more importantly — what it is not. Almost everyone gets this wrong, and examiners specifically test the misinterpretations
  • A confidence interval is a statement about the procedure, not about the parameter. Say it correctly once and it stays right forever
  • Simulate the Central Limit Theorem yourself in R (DTS 211): draw 1000 samples, plot the means, watch it become normal. Nothing else makes it as concrete
  • For every test, memorise the assumptions alongside the formula — "which test do I use here?" is the exam's favourite question

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