ETX5900 · Business Statistics
The Complete Exam Bible · S2 2026Business Statistics
ETX5900 Business Statistics is the postgraduate business-statistics unit taught by the Department of Econometrics and Business Statistics in Monash University's Faculty of Business and Economics. It builds the full inference toolkit a business analyst needs: describing data, quantifying uncertainty with probability and the normal and sampling distributions, estimating with confidence intervals, and then testing and modelling with the chi-square test, hypothesis testing, correlation and regression, and time-series forecasting. The unit runs as hands-on weekly workshops built around Excel (with R introduced late in the semester), and it assesses one skill above all at Monash University: taking a business question, choosing the correct statistical procedure, and defending the decision. Your mark comes from four tasks (in-class activities 15%, take-home quizzes 15%, a written assignment 20%, and the 50% final e-exam); a formula sheet and statistical tables are provided in the exam, so ETX5900 rewards judgement over memorisation. This guide mirrors the unit as taught, maps every chapter to its module, and uses the SWOTVAC run-in to rehearse method selection before the ~November 2026 exam period (confirm the exact date on Moodle / my.Monash). ETX5900 is a standard Monash postgraduate unit — confirm its credit-point value on Moodle / my.Monash so you can plan your workload across the semester.
What ETX5900 covers
ETX5900 Business Statistics builds in one direction: describe data, then quantify uncertainty, estimate, and finally test and model it. These twelve chapters follow the Monash teaching modules from descriptive statistics and probability, through the normal and sampling distributions and confidence intervals, into the chi-square test, hypothesis testing, correlation and regression, and time-series forecasting - each mapped to its module and to a slice of the 50% final e-exam.
How ETX5900 is assessed
| Component | Weight | Format |
|---|---|---|
| In-class activities / Exercise (Weeks 2-12, best 9 of 11, group) | 15% | In-workshop activities |
| Take-home Quizzes / Quiz-Test (Weeks 1-11, best 10 of 11, 1 attempt, 60 min) | 15% | Individual online quiz |
| Assignment (Written) Part A + Part B on supplied Excel dataset | 20% | Individual data-analysis report + quiz |
| Final Examination | 50% | Individual invigilated e-exam; formula sheet + stat tables provided; duration To be advised |
Two-tailed hypothesis test for a mean (sigma unknown, t-test)
- +1Step 1 - Hypotheses. Because the claim is about a difference in either direction, this is a two-tailed test: H0: mu = 45 versus H1: mu is not equal to 45, at significance level alpha = 0.05.
- +1Step 2 - Choose the statistic. The population sigma is unknown and is estimated by the sample s, so use the t-test with df = n - 1 = 19 (use t, not z, whenever sigma is unknown).
- +1Step 3 - Compute t. Standard error = s / √n = 6 / √20 = 6 / 4.472 = 1.342, so t = (x̄ − μ₀) / (s / √n) = (48 − 45) / 1.342 = 3 / 1.342 = 2.236.
- +1Step 4 - Critical value. Two-tailed at alpha = 0.05 puts alpha/2 = 0.025 in each tail; from the t table at df = 19 the critical values are plus or minus 2.093.
- +1Step 5 - Decision. Since |t| = 2.236 is greater than 2.093, the statistic falls in the upper rejection tail, so reject H0 (equivalently the two-tailed p-value is about 0.037, which is less than 0.05).
- +1Step 6 - Conclusion in context. There is sufficient evidence at the 5% level that the mean fill weight differs from 45 g; the sample points to over-filling. Note we say reject H0, never that H0 is proven true.
Key terms
- Population vs sample
- The population is the whole group of interest; a sample is the subset you actually measure. A numerical summary of a population is a parameter (e.g. mu, sigma); of a sample it is a statistic (e.g. x-bar, s).
- Standard deviation (s)
- A measure of spread: s = √(Σ(x − x̄)² / (n − 1)). The sample version divides by n − 1, not n. The coefficient of variation CV = (s / x̄) × 100% makes spread unit-free for comparison.
- Standard error
- The standard deviation of a sample statistic. For the sample mean it is σ / √n (or s / √n when σ is unknown) - it shrinks as the sample grows, which is why bigger samples give narrower intervals.
- Central Limit Theorem (CLT)
- For a large sample (rule of thumb n ≥ 30) the sampling distribution of x̄ is approximately normal regardless of the population shape, with mean μ and standard error σ / √n. It is what licenses z- and t-based inference.
- Confidence interval
- A range estimate for a parameter: estimate plus or minus (critical value x standard error). A 95% interval means 95% of such intervals over repeated samples would capture the true parameter - not a 95% probability for this one interval.
- z vs t
- Use z when the population sigma is known (or for a proportion); use the t-distribution with df = n - 1 when sigma is estimated by s. The t has heavier tails, so its critical values are larger - the price of estimating the spread.
- Null and alternative hypotheses
- H0 is the status-quo claim and always contains equality; H1 is the research claim. A test gathers evidence against H0; we either reject H0 or fail to reject it - we never accept or prove H0.
- One- vs two-tailed test
- Two-tailed (H1: not equal) splits alpha into both tails and rejects if |statistic| > critical value at alpha/2. One-tailed (H1: > or <) puts all of alpha in a single tail. The chi-square test is upper-tailed only.
- Type I and Type II errors
- A Type I error rejects a true H0 (its probability is alpha); a Type II error fails to reject a false H0 (probability beta). Power = 1 - beta. Lowering alpha raises beta - the two trade off.
- p-value
- The probability, if H0 were true, of a statistic at least as extreme as the one observed. The universal rule: reject H0 if p-value < alpha; otherwise do not reject.
- Chi-square test of independence
- Tests whether two categorical variables are related. Expected count f_e = (row total × column total) / n; statistic χ² = Σ(f_o − f_e)² / f_e on df = (r − 1)(c − 1); it is upper-tailed and needs every f_e ≥ 5.
- Least-squares regression
- Fits the line Ŷ = b₀ + b₁X that minimises the sum of squared vertical residuals. The slope b₁ = Σ(x − x̄)(y − ȳ) / Σ(x − x̄)², and b₀ = ȳ − b₁x̄.
- Coefficient of determination (R²)
- R² = SSR / SST = 1 − SSE / SST is the proportion of variation in Y explained by the model, between 0 and 1. In simple linear regression R² equals the square of the Pearson correlation r.
- MAD and MSFE
- Forecast-accuracy measures for time-series models: MAD = mean of |actual − forecast| and MSFE = mean of (actual − forecast)² . Lower is better; MSFE penalises large errors more heavily because the error is squared.
ETX5900 FAQ
Can AI help me study ETX5900?
Yes. Sia works through Business Statistics with you step by step: paste a workshop question or a past-style problem and Sia explains how to set it up - which test to choose (z vs t, one- vs two-tailed, chi-square, regression), how to state the hypotheses, how to read the standard-normal, t or chi-square table, and how to word the reject or fail-to-reject decision in context. It explains the reasoning at each step so you learn the method; it will not sit an assessment for you or hand over answers to work you must submit yourself.
Where can I find past exam papers or practice for ETX5900?
Official past papers and the mock e-exam are released inside your Monash Moodle unit for ETX5900, and the Monash Library exam paper collection is the place to check for prior papers - always confirm what is available on Moodle. To practise the same skills right now, this guide includes a full mini practice exam with fully worked solutions across every topic, and you can ask Sia to generate fresh practice questions in the Part A / B / C style and mark your working step by step.
What can Sia do that a textbook can't?
A textbook shows one worked example; Sia is interactive. It adapts to your exact question, re-explains a step a different way when you are stuck, generates unlimited fresh practice at the difficulty you need, and pinpoints why a specific slip (using z when sigma is unknown, halving alpha on a one-tailed test, the wrong df) cost the mark. It explains every step of the reasoning so you understand the method - it is a study aid, not a way to get assessment answers or a guaranteed grade.
Is ETX5900 hard?
It is a postgraduate business-statistics unit, so it moves quickly, but it is very learnable because it is procedural: almost every question is the same five-step framework (hypotheses, statistic, critical value, decision, conclusion) with a different distribution. Because a formula sheet and statistical tables are provided in the exam, the difficulty is in choosing the right procedure and interpreting the result, not in memorising algebra. Steady weekly practice on method selection is what makes it feel straightforward.
Is the ETX5900 exam open or closed book, and is there a hurdle?
The unit materials state that a formula sheet and statistical tables are provided in the final e-exam, but they do not state the open- vs closed-book status or the exam duration (listed as 'to be advised'), and the schedule notes a hurdle requirement as 'See Handbook' without a number. Do not assume any of these - confirm the book status, duration and any hurdle on Moodle and in the Monash Handbook / unit guide for your teaching period.
What is examined in ETX5900, and how much is the final worth?
The final examination is worth 50% of the unit - an individual, invigilated e-exam in the ~November 2026 end-of-semester period (confirm the date on Moodle). It draws across the whole unit: descriptive statistics, probability, the normal and sampling distributions, confidence intervals, the chi-square test of independence, hypothesis testing, correlation and regression, and time-series forecasting. The other 50% is within-semester work: in-class activities (15%), take-home quizzes (15%) and a written assignment (20%) in which the chi-square test is a core task.
How to study for the exam
Treat ETX5900 as a method-selection unit, not a memorisation unit - the exam provides the formula sheet and statistical tables. Week to week, keep the best-9-of-11 in-class activities and best-10-of-11 quizzes ticking over so the continuous 30% is banked, and start the 20% written assignment (with its core chi-square task on the supplied Excel dataset) early rather than in the final week. For the 50% final, drill the five-step framework until it is automatic: state H0 and H1, choose the distribution (z if sigma is known, t with df = n - 1 if not; z for a proportion using pi0; chi-square for two categorical variables; the slope t-test with df = n - 2 for regression), get the tail right, read the critical value, and finish with an explicit reject or fail-to-reject decision in context. Rehearse reading the standard-normal, t and chi-square tables, and do the mock e-exam under conditions to learn the Part A / B / C rhythm. Use SWOTVAC to practise picking the right test on mixed problems, and because the exam length is 'to be advised', practise a mark-proportional pace - spend time on each question in proportion to its marks, and confirm the duration on Moodle.
Your AI Statistics tutor for ETX5900
Stuck on a hard ETX5900 question? Sia is AskSia’s AI Statistics tutor — ask any ETX5900 Business Statistics question and get a clear, step-by-step explanation grounded in how the course is actually taught and assessed. Read this whole study guide free, then take your hardest questions to Sia.
