ETX5900 · Business Statistics
Past Exams & Revision
Past Exams & Revision is Week 12 of ETX5900 Business Statistics at Monash University — the synthesis week that turns the whole unit into an exam-ready routine rather than adding new theory. It is built around a mock e-exam, Part A / B / C past-paper practice and a formula-sheet drill for the final individual, invigilated e-exam worth 50% of the unit. The skill it rehearses is a single loop: read the question, pick the right test, read the provided tables at the correct α and df, and state the explicit reject / fail-to-reject decision in context.
What this chapter covers
- 01The exam blueprint: final individual invigilated e-exam worth 50%, sat in the ~November 2026 end-of-semester period (formula sheet + statistical tables provided; duration to be advised — confirm on Moodle)
- 02The Part A / B / C structure of the past papers and how marks are distributed across concepts, short calculations and extended data analysis
- 03The which-procedure decision map: estimation vs testing; mean vs proportion vs categorical vs numeric relationship
- 04The σ-known (z) vs σ-unknown (t, df = n−1) fork for a mean, and the two different standard errors for a proportion (CI uses p, test uses π₀)
- 05The five-step hypothesis-testing routine and the correct tail + reject rule for each test
- 06Reject rules stated correctly: two-tailed |stat| > crit_{α/2}, one-tailed single tail, chi-square upper-tail only, and the universal p < α rule
- 07One-sample z and t tests for a mean, and the z-test for a proportion
- 08The chi-square test of independence: f_e = row×col/total, χ² = Σ(f_o−f_e)²/f_e, df = (r−1)(c−1), reject if χ² > χ²_crit
- 09Simple linear regression: least-squares line, R², the slope t-test (df = n−2) and prediction inside the data range
- 10Exam traps and marking: reject vs fail-to-reject wording, matching direction words to the numbers, and mark-proportional pacing
Chi-square test of independence — are membership type and renewal related? (with the explicit decision)
- +1State the hypotheses. H₀: membership type and renewal are INDEPENDENT (no relationship); H₁: they are DEPENDENT (there is a relationship). Chi-square is an upper-tail test at α = 0.05.
- +2Expected counts f_e = row total × column total / grand total. Standard: 150×115/250 = 69 and 150×135/250 = 81. Premium: 100×115/250 = 46 and 100×135/250 = 54. Every f_e ≥ 5, so the chi-square approximation is valid.
- +1Test statistic. χ² = Σ(f_o−f_e)²/f_e = (60−69)²/69 + (90−81)²/81 + (55−46)²/46 + (45−54)²/54 = 1.1739 + 1.0000 + 1.7609 + 1.5000 = 5.435.
- +1Degrees of freedom and critical value. df = (r−1)(c−1) = (2−1)(2−1) = 1, so from the chi-square table χ²_{0.05,1} = 3.841 (upper tail only).
- +1Decision and conclusion. 5.435 > 3.841 (equivalently the p-value ≈ 0.020 < 0.05), so REJECT H₀. There is sufficient evidence at the 5% level that membership type and renewal are dependent — renewal behaviour differs between Standard and Premium members.
Key terms
- Null hypothesis (H₀)
- The status-quo / 'no effect' claim that always contains the equality (e.g. μ = μ₀, or 'the two variables are independent'). You either reject it or fail to reject it — you never 'accept' or 'prove' it.
- Test statistic
- A single number computed from the sample (z, t or χ²) that measures how far the data sit from H₀. Compared against a critical value from the provided tables, or summarised by a p-value.
- Critical value
- The table cut-off at level α (and the right df) that bounds the rejection region: z_{α/2}, t_{n−1,α/2} or χ²_{α,df}. Reject H₀ when the statistic lies beyond it.
- p-value
- The probability, if H₀ were true, of a test statistic at least as extreme as the one observed. The universal rule is: reject H₀ if p-value < α; otherwise fail to reject.
- Two-tailed vs one-tailed test
- A two-tailed test (H₁: ≠) rejects when |statistic| exceeds the α/2 critical value; a one-tailed test (H₁: > or <) puts the whole α in a single tail. Chi-square and the regression F-test are always upper-tail only.
- Type I and Type II error
- Type I is rejecting a true H₀ (probability α, the significance level); Type II is failing to reject a false H₀ (probability β). Power = 1 − β. Lowering α raises β for a fixed sample size.
- Chi-square test of independence
- Tests whether two categorical variables are related. Expected counts f_e = row×col/total; χ² = Σ(f_o−f_e)²/f_e on df = (r−1)(c−1); reject H₀ (independence) when χ² exceeds the upper-tail critical value.
- Formula sheet + statistical tables
- The List of Formulae and the standard-normal, Student-t and chi-square tables provided in the ETX5900 e-exam. Marks come from choosing the right formula and reading the table correctly, not from memorising them.
Past Exams & Revision FAQ
Is the ETX5900 final exam open-book, and how long is it?
The final assessment is an individual, invigilated e-exam worth 50% of the unit, sat in the ~November 2026 end-of-semester examination period. A formula sheet and the standard-normal, Student-t and chi-square tables are provided. The unit materials list the duration as 'To be advised' and do not state the open-/closed-book status, so confirm both the exact date and the exam conditions on Moodle / my.Monash before the day.
How do I decide which test to use in a Part B or Part C question?
Read three things off the question. First, are you estimating (build a confidence interval) or testing a claim (run a hypothesis test)? Second, is the target a mean, a proportion, a relationship between two categorical variables (chi-square), or between two numeric variables (regression slope test)? Third, for a mean, is the population σ given (use z) or only estimated by the sample s (use t with df = n−1)? Then state the tail and the reject rule before you compute, and finish with the explicit reject / fail-to-reject decision.
Can AI help me with past-exam revision in ETX5900?
Yes — Sia can explain a past-exam question step by step: why a scenario is a t-test rather than a z-test, how to read the chi-square table at df = (r−1)(c−1), or how to phrase a reject / fail-to-reject conclusion in context. Work your own practice numbers through it to build the selection habit the e-exam rewards. Sia explains and coaches the method; it does not sit your exam or promise guaranteed answers, grades or a pass.
Exam move
Revise ETX5900 as one decision loop rather than eleven separate topics: read the question, pick the procedure, read the provided table at the right α and df, compute the statistic, and state the explicit reject / fail-to-reject decision in context. Drill the forks that carry single marks — z vs t for a mean (σ known vs estimated by s, df = n−1), the two standard errors for a proportion (CI uses p, test uses π₀), and the tail for each test (two-tailed |stat| > crit_{α/2}, one-tailed single tail, chi-square upper-tail only). Rehearse the three test families the past papers lean on — a mean t-test, the chi-square test of independence, and the regression slope test — each end to end, showing every step so method marks survive an arithmetic slip. Because the formula sheet and statistical tables are provided, practise choosing and reading rather than memorising, and always finish with the decision line and a sentence whose direction matches the numbers. Since the exam duration is to be advised, budget your time in proportion to each question's marks and keep a reserve to check decisions and units — confirm the exam length and conditions on Moodle.
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