ECMT1010 Introduction to Economic Statistics
The Complete Exam Bible · S2 2026ECMT1010 Overview
- University of Sydney
- S2 2026
- 11 chapters
- Economics
ECMT1010 Introduction to Economic Statistics is the University of Sydney School of Economics' first-year gateway to statistics for economists — a MEGA-enrolment unit the course itself calls "one of the harder undergraduate units at the University of Sydney," recommending 6–8 hours of private study a week.
- Assessed by In-semester test (Week 7) subject to confirmation · Individual assignment subject to confirmation + 2 more
- Key terms Parameter vs statistic, Standard error (SE), Confidence interval, p-value
- How to prepare Treat ECMT1010 as a skills unit, not a memorisation unit: the formula sheet and tables are given, so your edge is fast, correct application.
- Most asked What does the Week-7 in-semester test cover and what is its format?
How ECMT1010 is assessed
| Component | Weight | Format |
|---|---|---|
| In-semester test (Week 7) | subject to confirmation | Closed-book, in-person, 1 hour writing + 5 min reading; 35 MCQ on a generalised answer sheet; non-programmable calculator; formula sheet + distribution tables supplied in the paper; covers Weeks 1–6 |
| Individual assignment | subject to confirmation | Individual data-analysis assignment using StatKey/Excel; due ~Week 11 (the captured run: 11.59pm Sydney time, Sun 24 May) |
| Final exam | subject to confirmation | In-person; short-answer Section B = 50 marks (~100 min suggested) plus an implied MCQ Section A; formula sheet + N(0,1)/t tables supplied in the paper; non-programmable calculator; covers the whole unit |
| Workshops / Muddy cards / participation | subject to confirmation | Weekly workshops (1–12) and the muddy-card feedback loop |
What ECMT1010 covers
The whole unit → one exam-ready map. Each topic links to its free chapter guide.
Sampling, Bias & Study Design
Week 1 · Lock5 Ch 1.1–1.3. Population vs sample, sampling bias, random sampling, association vs causation, confounders, observational vs experimental studies, randomization, blinding and the two-question decision tree.Week 1 sets the logic the whole unit runs on: we use a sample to make an inference about a population, and the two things that can break that inference are sampling bias (a non-random selection method) and confounding (a lurking third variable).
- Population vs sample, and inference; parameter (Greek) vs statistic (Latin)
- Sampling bias and why random sampling fixes it (the Dewey/Truman polling failure)
- Other biases: measurement, response and survivorship bias
- Association vs causation — and why association alone never proves cause
- Confounding variables: the lurking third variable that blocks a causal claim
- Observational study vs experimental study (random assignment + control)
Describing Data: Centre, Spread & Shape
Week 2 · Lock5 Ch 2.1–2.5. Categorical vs quantitative, histograms and skew, mean/median, SD/IQR, the five-number summary, boxplots, the 1.5×IQR outlier rule, z-scores, the 95% rule and correlation r.Week 2 is the toolkit for summarising one or two variables: centre (mean vs median and resistance to outliers), spread (SD, range, IQR and the five-number summary), shape (symmetric vs skewed histograms), location (z-scores) and association (the correlation r).
- Categorical vs quantitative variables, and choosing the right summary
- Histograms and shape: symmetric vs left/right-skewed; how skew pulls the mean
- Centre: mean x̄ vs median; the median is resistant to outliers, the mean is not
- Spread: standard deviation s, range, IQR and the five-number summary
- Boxplots and the 1.5×IQR rule for flagging outliers
- Standardisation: the z-score zᵢ = (xᵢ − x̄)/s as 'distance from the mean in SDs'
Confidence Intervals & the Bootstrap
Weeks 3–4 · Lock5 Ch 3.1–3.4. Sampling distribution, standard error, the confidence interval (statistic ± 2·SE), interpreting a CI, the bootstrap (resample with replacement), the percentile method and when the bootstrap fails.Weeks 3–4 move from describing a sample to estimating a parameter with uncertainty attached.
- The sampling distribution: how a statistic varies across all possible samples
- Standard error (SE) = the SD of the sampling distribution; bigger SE = less reliable
- The interval estimate = statistic ± margin of error (ME)
- The 95% confidence interval = statistic ± 2·SE, and the general statistic ± z*·SE
- Correct vs incorrect interpretation of a confidence level (the procedure, not the parameter)
- The bootstrap: resample WITH replacement to build a bootstrap distribution and read off the SE
Hypothesis Testing & Randomization
Weeks 5–6 · Lock5 Ch 4.1–4.5, 5.1. Null vs alternative hypotheses, the randomization distribution, the p-value, significance level α, one- vs two-sided tests, the CI↔HT link and Type I / Type II errors and power.Weeks 5–6 build the formal test of evidence: state a null and an alternative hypothesis in population parameters, build a randomization distribution in StatKey under a true H₀, read off the p-value, and decide against the significance level α.
- Null H₀ (contains '=') vs alternative Hₐ (>, <, or ≠), always in population parameters
- The randomization distribution: simulate statistics from a world where H₀ is true
- Reallocate (experiments) vs shift/shuffle (observational) to make H₀ true
- The p-value: probability of a result this extreme (or more) if H₀ is true
- One-sided (one tail) vs two-sided (both tails) p-values
- Significance level α: p < α → reject H₀ (significant); p > α → inconclusive
The Normal Distribution & the CLT
Weeks 6 & 8 · Lock5 Ch 4.3–4.5, 5.2, 6.1. The normal density, the standard normal N(0,1), z = (x−μ)/σ, reading areas and percentiles, the Central Limit Theorem, CLT conditions and the z* critical values 1.645/1.960/2.576.Weeks 6 and 8 are the bridge from simulation to formulas.
- The normal density: symmetric, bell-shaped, with inflection points at μ ± σ
- The standard normal N(0,1) and standardising z = (x − μ)/σ; back-converting x = μ + z·σ
- Reading areas (probabilities) and percentiles from the N(0,1) table
- The Central Limit Theorem: the sampling distribution of a mean/proportion is ≈ normal for large n
- CLT conditions: n ≥ 30 for a mean; np ≥ 10 and n(1 − p) ≥ 10 for a proportion
- The SD of the sample mean SD(X̄) = σ/√n, and why bigger n means a tighter distribution
Inference for Proportions
Weeks 8–9 · Lock5 Ch 6.1, 6.5. The SE for a proportion √(p(1−p)/n), the CI and HT for one proportion, the difference in two proportions, the pooled p̂ for the two-proportion test and the CLT conditions.Weeks 8–9 apply the normal-formula machinery to categorical data: the SE for a proportion √(p(1−p)/n), the CI for one proportion p̂ ± z*·SE, the z-test for one proportion, and the two-proportion test that uses a pooled p̂ under H₀: p₁ = p₂.
- The SE for a proportion (CLT formula): SE = √(p(1 − p)/n)
- CI for one proportion: p̂ ± z*·√(p̂(1 − p̂)/n), valid when np̂ ≥ 10 and n(1 − p̂) ≥ 10
- HT for one proportion: z = (p̂ − p₀)/√(p₀(1 − p₀)/n) — use the NULL value p₀ in the SE
- Why the CI uses p̂ but the test uses p₀ (the SE is computed under the assumed truth)
- Difference in two proportions: SE = √(p̂₁(1 − p̂₁)/n₁ + p̂₂(1 − p̂₂)/n₂) for a CI
- The pooled proportion p̂ = (count₁ + count₂)/(n₁ + n₂) for the two-proportion TEST
Inference for Means: One-, Two-Sample & Paired
Week 9 · Lock5 Ch 6.2–6.4. The t-distribution and df, the CI and HT for one mean, the difference in two means, paired vs independent data and why pairing raises power.Week 9 does for quantitative data what the previous chapter did for proportions, but with the t-distribution (used whenever σ is unknown).
- The t-distribution and degrees of freedom; why t (not z) when σ is unknown
- CI for one mean: x̄ ± t*(df, α/2)·(s/√n), df = n − 1
- HT for one mean: t = (x̄ − μ₀)/(s/√n) ~ t(n − 1)
- Difference in two independent means: SE = √(s₁²/n₁ + s₂²/n₂), t = (x̄₁ − x̄₂)/SE
- The conservative df rule for two means: df = min(n₁, n₂)
- Paired data: form per-pair differences d, then run a one-sample t on d̄
Simple Linear Regression
Week 10 · Lock5 Ch 2.6, 9.1–9.2. The least-squares line ŷ = b₀ + b₁x, the slope b₁ = r·(sy/sx), residuals, interpreting slope/intercept, inference for the slope (t, df = n−2), R² = r² and the ANOVA decomposition.Week 10 models a straight-line relationship between two quantitative variables: the least-squares line ŷ = b₀ + b₁x, with slope b₁ = r·(sy/sx), the meaning of the slope and intercept, residuals, inference for the slope (t with df = n − 2), and goodness of fit via R² = r² and the ANOVA decomposition.
- The least-squares line ŷ = b₀ + b₁x, fitted to minimise Σ(yᵢ − ŷᵢ)²
- Slope b₁ = r·(sy/sx) and intercept b₀ = ȳ − b₁·x̄
- Interpreting the slope (change in ŷ per 1-unit x) and intercept (ŷ at x = 0)
- Residuals eᵢ = yᵢ − ŷᵢ and the extrapolation warning (only predict within the x range)
- Inference for the slope: t = b₁/SE(b₁), df = n − 2, and a CI for β₁
- The correlation test t = r√(n − 2)/√(1 − r²) on df = n − 2
Probability
Week 11 · Lock5 Ch P.1–P.2. Sample space and events, the Kolmogorov axioms, complement, addition, conditional probability, the multiplication rule, independence, total probability and Bayes' rule.Week 11 starts the 'why it works' theory block with the rules of probability: the sample space and events, the Kolmogorov axioms, the addition and multiplication rules, conditional probability, the difference between independence and mutual exclusivity, the law of total probability and Bayes' rule.
- Experiment, sample space Ω and event; equally-likely outcomes P(A) = |A|/|Ω|
- The Kolmogorov axioms: P(A) ≥ 0, P(Ω) = 1, additivity for disjoint events
- The complement rule: P(Aᶜ) = 1 − P(A)
- The addition rule: P(A or B) = P(A) + P(B) − P(A and B)
- Conditional probability P(A|B) = P(A and B)/P(B) and the multiplication rule
- Independence vs mutual exclusivity (and why they are not the same)
Random Variables & Distributions
Week 12 · Lock5 Ch P.3–P.5. The discrete pmf, expected value E[X] and EV rules, variance and SD of a random variable, the binomial distribution, continuous RVs, the pdf and area-as-probability.Week 12 turns probability into numbers attached to outcomes.
- Discrete random variable and its pmf p(x), with Σp(x) = 1
- Expected value E[X] = Σxᵢpᵢ as a probability-weighted average (the mean μ_X)
- EV rules: E[X + Y] = E[X] + E[Y], E[bX] = b·E[X], E[b] = b, and E[g(X)] = Σg(xᵢ)pᵢ
- Variance Var(X) = E[(X − μ)²] = E[X²] − μ², and SD σ_X = √Var(X)
- The binomial distribution P(X = k) = C(n, k)pᵏ(1 − p)ⁿ⁻ᵏ
- Binomial mean np and SD √(np(1 − p))
Covariance & the Theory of Estimators
Week 13 · lecture-only capstone. Covariance cov(X,Y) and correlation ρ, the covariance and variance rules, the estimator X̄ vs the estimate x̄, E(X̄)=μ and Var(X̄)=σ²/n, and the bridge to ECMT1020.Week 13 is the lecture-only capstone that explains why the earlier methods work.
- Population covariance cov(X, Y) = σ_XY = E[(X − μ_X)(Y − μ_Y)] and its sign
- Population correlation ρ_XY = σ_XY/(σ_X·σ_Y), the unit-free version of covariance
- Independence ⇒ cov = 0 (and why the converse need not hold)
- Covariance rules: cov(X, V + W) = cov(X, V) + cov(X, W); cov(X, bZ) = b·cov(X, Z); cov(X, b) = 0
- Variance rules: Var(V + W) = Var(V) + Var(W) + 2cov(V, W); Var(bZ) = b²Var(Z); Var(b) = 0
- Estimator vs estimate: X̄ as a random variable (before) vs x̄ as a number (after)
It runs a modern simulation track (the bootstrap and randomization in StatKey) alongside the classical formula/CLT track, then turns to probability theory and random variables, all built on the free Lock5 text (Statistics: Unlocking the Power of Data) and worked in StatKey and Excel.
It is assessed by a closed-book in-semester test in Week 7 (35 MCQ covering Weeks 1–6), an individual data-analysis assignment, and a final exam whose short-answer Section B is worth 50 marks.
Both the test and the exam supply the formula sheet and the N(0,1) and t distribution tables in the paper — so marks are not lost on recall but on choosing the wrong test, fumbling the H₀/Hₐ setup, misreading the table for the right df and tail, or skipping the one-sentence conclusion in context.
(Exact component weights and the official exam date are subject to confirmation — the LMS pull did not capture the assessment-information page or a published timetable; confirm in your unit outline.)
Worked example · free
One-mean t-test with the provided formula sheet (final exam, Section B style)
- 2 marksDefine the parameter and state the hypotheses in population terms. Let μ = the true mean fill weight (g). Because the concern is under-filling, run a one-sided (left) test: H₀: μ = 250 versus Hₐ: μ < 250.
- 1 markChoose the right method. The population SD σ is unknown and we have one quantitative sample, so use the one-sample t-statistic with df = n − 1 = 24 (the exam supplies the t table).
- 1 markCompute the standard error: SE = s/√n = 6/√25 = 6/5 = 1.2 g.
- 2 marksCompute the test statistic: t = (x̄ − μ₀)/(s/√n) = (247.4 − 250)/1.2 = −2.6/1.2 ≈ −2.17.
- 1 markApply the decision rule. The one-sided 5% critical value from the t table is t(24) ≈ −1.711. Since −2.17 < −1.711, the statistic falls in the rejection region (equivalently the p-value < 0.05).
- 1 markConclude in context: reject H₀. There is significant evidence at the 5% level that the mean bag weight is below 250 g, so the bags appear to be under-filled.
Key terms
- Parameter vs statistic
- A parameter is a numerical summary of a whole population, written in Greek (μ, σ, p, ρ); a statistic is the matching summary computed from a sample, written in Latin (x̄, s, p̂, r). Inference uses the statistic to estimate the unknown parameter.
- Standard error (SE)
- The standard deviation of a sample statistic across all possible samples. For a sample mean it is σ/√n (estimated by s/√n); it shrinks as n grows, which is why larger samples estimate more precisely. The bootstrap estimates the SE from a single sample.
- Confidence interval
- An interval of the form statistic ± z*·SE (or statistic ± 2·SE for 95%) that, over repeated sampling, captures the true parameter a stated percentage of the time. '95% confident' refers to the long-run procedure (19 of 20 samples), not a probability about one fixed interval.
- p-value
- The probability of getting a statistic as extreme as — or more extreme than — the one observed, assuming H₀ is true. If the p-value < α you reject H₀ ('statistically significant'); if it exceeds α the result is inconclusive.
- Central Limit Theorem (CLT)
- For a large enough sample (rule of thumb n ≥ 30 for a mean; np ≥ 10 and n(1−p) ≥ 10 for a proportion) the sampling distribution of the statistic is approximately normal regardless of the population's shape, which justifies the normal- and t-based formula procedures.
ECMT1010 FAQ
Is ECMT1010 hard?
The unit itself flags it as 'one of the harder undergraduate units at the University of Sydney' and recommends 6–8 hours of private study a week on top of the lecture and workshop.
The difficulty is structural, not arithmetic: it runs a modern simulation track (the bootstrap and randomization in StatKey) alongside the classical formula/CLT track and then takes a hard probability-theory turn in Weeks 11–13. Keeping up weekly and drilling the 'choose-the-right-test → set it up → conclude in context' ritual is what gets students through.
Do I need to memorise the formulas?
No. Both the Week-7 in-semester test and the final exam supply the formula sheet and the N(0,1) and t distribution tables bound into the paper. The marks come from choosing the right method, defining notation and H₀/Hₐ in population parameters, substituting correctly, reading the table for the right df and tail, and writing the one-sentence conclusion in context — so practise application, not rote recall.
What does the Week-7 in-semester test cover and what is its format?
The in-semester test is closed-book, in-person, 1 hour of writing plus 5 minutes reading time, and consists of 35 multiple-choice questions on a generalised answer sheet. It covers Weeks 1–6 (sampling and study design, descriptive statistics, confidence intervals and the bootstrap, and hypothesis testing and randomization).
A non-programmable calculator is permitted and the formula sheet and distribution tables are printed in the paper.
Can I use StatKey, Excel and a calculator in the exam?
StatKey and Excel are your everyday learning, homework and assignment tools — StatKey for the bootstrap, randomization and distribution areas, Excel (with the Data Analysis ToolPak) for EDA and regression — but there is no computer in the exam room. In the closed-book test and final you bring an approved non-programmable calculator and work by hand using the provided formula sheet and N(0,1)/t tables.
How is ECMT1010 assessed overall and are the weights confirmed?
The grounded components are a closed-book Week-7 in-semester test (35 MCQ on Weeks 1–6), an individual data-analysis assignment due around Week 11, a final exam with a 50-mark short-answer Section B (and an implied MCQ Section A), plus weekly workshops and muddy cards.
The exact percentage weights and the official exam date were not in the LMS pull, so they are subject to confirmation — check your current unit outline for the authoritative numbers.
Questions students ask in each ECMT1010 chapter
- Why does random sampling matter so much?
- Because the whole point of the unit is to generalise from a sample to a population, and that only works if the sample is representative. A non-random selection method introduces sampling bias — the classic example is a poll that systematically over-samples one type of voter and so calls the election wrong. Random sampling gives every member of the population a chance of selection, so on average the sample mirrors the population. Chapter 01 · Sampling, Bias & Study Design
- When should I report the median instead of the mean?
- Use the median when the data are skewed or contain outliers, because it is resistant — it ignores how extreme the tail values are and reports the true middle. The mean is pulled toward the long tail, so for skewed data like incomes or house prices the mean overstates the 'typical' value. For roughly symmetric data the mean and median are close and the mean is fine. Chapter 02 · Describing Data: Centre, Spread & Shape
- What exactly does '95% confident' mean?
- It is a statement about the method, not about this one interval. If you repeated the whole sampling-and-interval procedure many times, about 95% of the intervals you produced would contain the true parameter. The parameter is a fixed (unknown) number, so it is either in your particular interval or it is not — there is no probability about it. Always phrase the interpretation as 'we are 95% confident the interval contains…'. Chapter 03 · Confidence Intervals & the Bootstrap
- What does the p-value actually tell me?
- It tells you how surprising your data would be if the null hypothesis were true — specifically, the probability of a statistic at least as extreme as the one you observed under H₀. A small p-value means 'data like this rarely happens when H₀ holds', which is evidence against H₀. It is NOT the probability that H₀ is true, and it is NOT the probability you made a mistake. Chapter 04 · Hypothesis Testing & Randomization
- What is the difference between σ and σ/√n?
- σ is the standard deviation of individual values in the population — how spread out single observations are. σ/√n is the standard deviation of the sample mean (often called its standard error) — how much the average of n observations bounces around. The mean is far less variable than an individual value, which is why σ/√n shrinks as n grows. Use σ for a question about one value and σ/√n for a question about a sample average. Chapter 05 · The Normal Distribution & the CLT
- Why does the one-proportion test use p₀ in the SE but the CI uses p̂?
- Because the standard error must be computed under the relevant assumption. A hypothesis test asks 'how surprising is this data IF H₀ is true?', so the sampling distribution — and hence the SE — is built using the assumed null value p₀: SE = √(p₀(1 − p₀)/n). A confidence interval makes no such assumption; it just estimates the true proportion, so it uses your best estimate p̂: SE = √(p̂(1 − p̂)/n). Chapter 06 · Inference for Proportions
- When do I use t instead of z?
- Use t whenever you are doing inference about a mean and the population standard deviation σ is unknown — which is essentially always with real data, because you only have the sample SD s. The t-distribution has fatter tails than z to account for the extra uncertainty from estimating σ, and it depends on the degrees of freedom. In ECMT1010 the means chapter is entirely t-based; z is reserved for proportions and for large-sample normal approximations. Chapter 07 · Inference for Means: One-, Two-Sample & Paired
- How do I interpret the slope and intercept correctly?
- The slope is the predicted change in y for a one-unit increase in x, stated in the real units of both variables and with the right sign — e.g. '+$1,400 of revenue per extra $1,000 of ad spend'. The intercept is the predicted y when x = 0; it is only meaningful if x = 0 is sensible and within the data range, otherwise it is just where the line crosses the axis (often an extrapolation) and should not be over-interpreted. Chapter 08 · Simple Linear Regression
- What is the difference between independent and mutually exclusive events?
- Independence is about information: A and B are independent if knowing one happened does not change the probability of the other (P(A|B) = P(A), so P(A and B) = P(A)·P(B)). Mutual exclusivity is about overlap: A and B are mutually exclusive if they cannot both occur, so P(A and B) = 0. They are different — in fact two events with positive probability that are mutually exclusive are necessarily dependent, because if one happens the other definitely cannot. Chapter 09 · Probability
- What is the difference between expected value and a plain average?
- A plain average treats every value equally; expected value weights each possible value by its probability: E[X] = Σxᵢpᵢ. If the outcomes are equally likely the two coincide, but when some values are more probable than others — like a pricing tier with many more cheap subscribers than expensive ones — the expected value is pulled toward the high-probability values. It is the long-run average you would see over many repetitions, not the simple midpoint of the possible values. Chapter 10 · Random Variables & Distributions
- What is the difference between an estimator and an estimate?
- An estimator is a rule or formula applied to a sample — for the mean it is X̄ = (1/n)ΣXᵢ — and before you collect data it is a random variable with its own distribution, mean and variance. An estimate is the single number you get once you plug in your actual sample, written with a lowercase x̄. The estimator is the random recipe; the estimate is the realised dish. This distinction is what lets us talk about the estimator being unbiased (E(X̄) = μ) and having variance σ²/n even before any data are collected. Chapter 11 · Covariance & the Theory of Estimators
How to study for the exam
Treat ECMT1010 as a skills unit, not a memorisation unit: the formula sheet and tables are given, so your edge is fast, correct application. (1) Keep up weekly — at 6–8 hours of private study the content compounds, and the two tracks (simulation via StatKey and the classical formula/CLT method) must both be fluent because the exam mixes them.
(2) Build a 'name-the-right-test' decision habit: for every question first classify the data and the goal — describe it, estimate it with a CI, test a hypothesis, or model it with regression — then ask one mean, two means, paired, one proportion, two proportions, or a regression slope before you pick a formula.
(3) Map the provided formula sheet and the N(0,1)/t tables so exam time goes to setup and reading the right df and tail, not searching. (4) Rehearse the Section-B ritual: parameter definition → H₀/Hₐ in population parameters → formula in symbols → substitution → table value with df and tail → decision rule → one-sentence conclusion in context; partial marks reward every step.
(5) Use StatKey to build intuition for sampling distributions, bootstraps and randomization, and Excel for EDA and regression, but rehearse the by-hand table method the closed-book exam actually uses. (6) The Week-7 test is your dress rehearsal for Weeks 1–6 — review it carefully because those foundations resurface in the final.
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