26134 Responsible Evidence-Based Decisions
The Complete Exam Bible · Spring 202626134 Overview
- University of Technology Sydney
- Spring 2026
- 12 chapters
- Statistics
26134 Responsible Evidence-Based Decisions is the University of Technology Sydney's first-year, core business-statistics subject (formerly "Business Statistics") in the UTS Business School, and it is worth 6 credit points toward your Weighted Average Mark (WAM). This subject runs across five modules over the session.
- Assessed by Online quizzes (best 4 of 6 count) 20% · Group assignment 30% · Final examination 50%
- Key terms Descriptive vs inferential statistics, Standard error (SE), Confidence interval, Test statistic
- How to prepare Treat 26134 as a toolbox of about a dozen small methods rather than one long reading…
- Most asked Where can I find past exam papers / practice for 26134?
How 26134 is assessed
| Component | Weight | Format |
|---|---|---|
| Online quizzes (best 4 of 6 count) | 20% | Individual online Canvas quizzes released across the session (six quizzes; best four count) |
| Group assignment | 30% | Group data-analysis project submitted via Canvas (weight is the standard structure — confirm current-session weight on the UTS subject outline) |
| Final examination | 50% | 120-minute restricted open-book online exam (ProctorU-invigilated); 25 equally-weighted questions presented all at once; calculator and offline notes/Excel permitted, no internet |
What 26134 covers
26134 runs across five modules over the UTS session, building from describing data to drawing inferences from it. You start with descriptive statistics and data communication, move through probability and the binomial and normal distributions, then into sampling distributions, confidence intervals, hypothesis testing and regression, and finish with the ethical use of data.
It is assessed by six online quizzes (best four count, 20%), a group assignment (30%) and a 120-minute restricted open-book final exam worth 50%.
Exploring Data: Descriptive Statistics
Data types, central tendency, spread, distribution shape · (Week 1)Week 1 opens Module 1: how to summarise a raw dataset before you infer anything from it.
- Qualitative (nominal, ordinal) vs quantitative (discrete, continuous) variables and the four measurement scales
- Frequency, relative-frequency and cumulative-frequency tables; choosing class widths for a histogram
- Central tendency: mean x̄ = (Σxᵢ)/n, median (middle order statistic), mode
- Spread: range, sample variance s² = Σ(xᵢ − x̄)²/(n − 1), standard deviation s = √s²
- Coefficient of variation CV = (s/x̄) × 100% for comparing dispersion across scales
- Distribution shape: symmetric, right-skew (mean > median), left-skew, bimodal, uniform, J-shaped
Communicating Insights from Data
Choosing charts, visualisation, honest presentation · (Week 2)Week 2 completes Module 1 by pairing description with honest communication: which chart suits which data, the principles of good visual design, and the classic ways graphs mislead.
- Choosing a chart: bar chart (categorical), histogram (grouped numerical), scatterplot (two numerical), and why pie charts are often a poor choice
- Correlation: Pearson r = cov(x,y)/(sₓs_y), range −1 to +1, measures LINEAR association only
- Correlation ≠ causation and spurious correlation
- The truncated-axis fallacy: bar charts must start the y-axis at zero
- Percentage points vs percent (relative) change; absolute vs relative risk
- Exploratory vs explanatory messaging; knowing your data before you present
Predicting Events: Probability Foundations
Sample space, joint & conditional probability, Bayes, independence · (Week 3)Week 3 begins the bridge from describing data to inferring from it.
- Classical, relative-frequency and subjective probability; axioms 0 ≤ P(A) ≤ 1 and P(S) = 1
- Sample space, events, and reading a contingency table
- Marginal P(A), joint P(A ∩ B) and union P(A ∪ B) probabilities
- Complement rule P(Aᶜ) = 1 − P(A) and addition rule P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
- Mutually exclusive vs collectively exhaustive events
- Conditional probability P(A | B) = P(A ∩ B)/P(B) and the multiplication rule
Discrete Outcomes: The Binomial Distribution
Random variables, binomial pmf, expectation, binomial table · (Week 4)Week 4 formalises discrete random variables and their distributions, centred on the binomial.
- Discrete random variable, PMF P(X = x) with 0 ≤ P ≤ 1 and ΣP = 1, and the CDF F(x) = P(X ≤ x)
- Expected value E(X) = Σx·P(X = x) and variance Var(X) = Σ(x − μ)²·P(X = x)
- Bernoulli trial: one trial, success p, mean p, variance p(1 − p)
- Binomial conditions: fixed n, two outcomes, constant p, independent trials
- Binomial PMF P(X = x) = C(n,x)·pˣ·(1 − p)^(n−x)
- Binomial mean μ = np, variance σ² = np(1 − p), SD σ = √(np(1 − p))
Continuous Outcomes: The Normal Distribution
Densities, standard normal, Z-scores, the Z-table · (Week 5)Week 5 moves to continuous random variables, where probability is area under a density curve, and to the normal distribution in particular. You standardise to Z-scores and use the Z-table to find tail and interval probabilities.
- Continuous random variable and probability density function f(x): probability = area, total area = 1
- Why P(X = an exact value) = 0 for a continuous variable
- The normal distribution N(μ, σ²): bell-shaped, symmetric, mean = median = mode
- The empirical 68–95–99.7 rule
- Standardisation to a Z-score: Z = (X − μ)/σ, giving Z ~ N(0, 1)
- Reading the Z-table for P(Z ≤ z), and using symmetry for lower and upper tails
Insights from Limited Information: Sampling Distributions
Population vs sample, sampling distribution of the mean, CLT · (Week 6)Week 6 opens Module 2 with the key idea behind all inference: a sample statistic is itself a random variable.
- Population parameter (μ, σ, p — fixed, unknown) vs sample statistic (x̄, s, p̂ — random)
- A statistic is a random variable: it varies from sample to sample
- Sampling distribution of the sample mean: E(x̄) = μ
- Standard error of the mean SE = σ/√n and why it shrinks as n grows
- Central Limit Theorem: x̄ is approximately normal for large n regardless of population shape (rule of thumb n ≥ 30)
- Standardising the sample mean: Z = (x̄ − μ)/(σ/√n) when σ is known
Estimating Population Values: Confidence Intervals
Point vs interval estimation, t-distribution, CIs, t-table · (Week 7)Week 7 completes Module 2: estimating a population mean with an interval, not just a point.
- Point estimate (x̄ for μ) vs interval estimate (a confidence interval)
- Confidence level 1 − α, and the general form point estimate ± critical value × standard error
- CI for a mean, σ known: x̄ ± z_(α/2)·σ/√n (z* = 1.645, 1.96, 2.576 for 90/95/99%)
- CI for a mean, σ unknown: x̄ ± t_(α/2, n−1)·s/√n, reading the t-table with n − 1 df
- Correct interpretation: the procedure captures μ in 1 − α of repeated samples
- The common misinterpretation to avoid (not 'a 95% chance μ is in this interval')
Testing Ideas I: Hypothesis-Testing Foundations
Null vs alternative, test statistic, p-value, Type I/II errors · (Week 8)Week 8 opens Module 3 with the one-sample hypothesis test, the template every later test reuses.
- Null hypothesis H₀ (contains the equality) vs alternative H₁ (two-, left- or right-tailed)
- Test statistic as a standardised distance from the H₀ value
- Significance level α and the rejection region beyond the critical value
- p-value: probability of a statistic at least as extreme as observed if H₀ is true; reject if p ≤ α
- One-tailed vs two-tailed tests (α vs α/2 in each tail)
- z-test for a mean, σ known: z = (x̄ − μ₀)/(σ/√n)
Testing Ideas II: Comparing Groups
Two-sample & paired t-tests, ANOVA, F-test, decision tree · (Week 9)Week 9 extends hypothesis testing to comparisons: the two-independent-samples t-test (with its equal-variance assumption), the paired-samples t-test as a one-sample test on differences, ANOVA for more than two groups, and the F-test for equal variances.
- Two independent samples, difference in means: pooled variance s²_p and t with df = n₁ + n₂ − 2
- Equal-variance assumption for the pooled t-test
- Paired (dependent) samples: reduce to a one-sample t-test on the differences dᵢ, df = n − 1
- Recognising paired vs independent designs (before/after on the same units = paired)
- ANOVA for more than two means: SST = SSB + SSW, F = MSB/MSW
- F-test for equal variances: F = s₁²/s₂² (larger over smaller), df = (n₁ − 1, n₂ − 1)
Modelling Relationships: Regression Analysis
Scatter, least-squares line, slope/intercept, fit, inference · (Week 10)Week 10 is Module 4: simple linear regression. You read a scatterplot, fit the least-squares line, interpret the slope and intercept, assess goodness of fit with R², and reason about confounding and the difference between correlation and a causal effect.
- The model yᵢ = β₀ + β₁xᵢ + εᵢ and the fitted line ŷ = b₀ + b₁x
- Least-squares estimation: minimise Σ(yᵢ − ŷᵢ)²
- Slope b₁ = r·(s_y/sₓ) = Σ(xᵢ − x̄)(yᵢ − ȳ)/Σ(xᵢ − x̄)²
- Intercept b₀ = ȳ − b₁x̄; the line passes through (x̄, ȳ)
- Interpreting the slope (change in y per unit x) and intercept (y at x = 0)
- Goodness of fit: R² = SSR/SST = 1 − SSE/SST; in simple regression R² = r²
Ethical Use of Data
Principles vs rules, ethical frameworks, Five Safes, privacy · (Week 11)Week 11 is Module 5, the 'responsible' half of the subject's name, and it is fully examinable short-answer territory.
- Rule-based (clarity, consistency, compliance) vs principle-based (flexibility, judgement) approaches
- The four ethical principles: respect for persons, beneficence, justice, respect for law and public interest
- Respect for persons and informed consent; extra protection for those with diminished autonomy
- Consequentialist (judge by outcomes) vs deontological (judge by duties/means) frameworks
- Anonymisation / de-identification, secure data handling, and re-identification risk
- The Five Safes framework: safe projects, people, settings, data, outputs
Exam Preparation: The Restricted Open-Book Exam
25 equal-mark Qs, 120 min, tables + Excel, timing · (Week 12)Week 12 consolidates Modules 1–5 for the final: the exam format (120 minutes, 25 equally-weighted questions presented all at once, restricted open-book, no negative marking), how to pre-organise the Z/t/chi-square/F/binomial tables and your notes for speed, and a decision tree that routes any question to the right method.
- Exam format: 120 minutes, 25 equally-weighted questions presented all at once, no negative marking
- Restricted open-book: paper notes, textbook, a calculator of any type and offline Excel/Word/PDF allowed; no internet or cloud notes
- Delivery via ProctorU (Guardian browser); on-campus sitting can be requested
- Pre-loading and navigating the five statistical tables (Z, t, chi-square, F, binomial)
- A master decision tree: describe vs infer, one vs two samples, mean vs variance, Z vs t, paired vs independent
- Time budgeting: roughly one question every four to five minutes with a review buffer
Module 1 is descriptive statistics and data communication (Weeks 1-2): data types, measures of central tendency and spread, distribution shape, choosing honest charts. Weeks 3-5 bridge to inference through probability, the binomial distribution and the normal distribution. Module 2 is inferential statistics (Weeks 6-7): sampling distributions, the Central Limit Theorem and confidence intervals.
Module 3 is hypothesis testing (Weeks 8-9): one-sample tests, then two-sample, paired, ANOVA and F-tests, routed with a decision tree. Module 4 is simple linear regression (Week 10), and Module 5 is the ethical use of data (Week 11).
It is a method-and-interpretation subject: nearly every item asks you to pull a value from a scenario or table, apply one formula or table lookup, and state a decision or a one-line responsible interpretation.
Assessment runs through Canvas as six online quizzes (best 4 of 6 count, 20%), a group data-analysis assignment (30% — confirm the current-session weight on the UTS subject outline) and a 120-minute restricted open-book final examination worth 50%.
The final is invigilated online through ProctorU: 25 equally-weighted questions presented all at once, with paper notes, a calculator of any type and offline Excel permitted (no internet, no cloud notes), and no negative marking applies. UTS grades on the HD / D / C / P scheme, and the UTS academic-integrity policy governs every component.
26134 cheatsheet for the final exam
AskSia publishes a free 26134 cheatsheet for the final exam, a cheat sheet that follows the official permitted-materials rule for this assessment and condenses the topics in this guide. Open the 26134 cheatsheet.
Worked example · free
One-sample t-test for a mean (population SD unknown)
- +1State the hypotheses and pick the statistic. H₀: μ = 40 versus H₁: μ ≠ 40 (two-tailed). The population SD σ is unknown and n is small, so use a one-sample t-test with df = n − 1 = 15 and read the t-table.
- +1Compute the standard error of the mean: SE = s / √n = 9.0 / √16 = 9.0 / 4 = 2.25 hours.
- +1Compute the test statistic: t = (x̄ − μ₀) / SE = (44.5 − 40) / 2.25 = 4.5 / 2.25 = 2.00 on 15 degrees of freedom.
- +1Decide against the critical value. For a two-tailed test at α = 0.05, t₀.₀₂₅,₁₅ = 2.131 from the t-table. Since |t| = 2.00 < 2.131, the statistic falls outside the rejection region, so fail to reject H₀ (p-value > 0.05).
Key terms
- Descriptive vs inferential statistics
- Descriptive statistics summarise a dataset you have (mean, spread, shape, charts); inferential statistics use a sample to draw conclusions about a population you cannot fully observe (estimation and hypothesis testing). 26134 spends Module 1 on the first and Modules 2-4 on the second.
- Standard error (SE)
- The standard deviation of a sample statistic across all possible samples. For the sample mean, SE = σ/√n (or s/√n when σ is unknown). It shrinks as n grows, which is why larger samples give tighter confidence intervals and more powerful tests.
- Confidence interval
- An interval estimate point estimate ± (critical value) × SE that is built by a procedure which captures the true parameter in a proportion 1 − α of repeated samples. A 95% CI does NOT mean a 95% probability the parameter lies in this one interval — the parameter is fixed and the interval is random.
- Test statistic
- A standardised distance of the sample estimate from the value assumed under H₀ (a z, t, χ² or F). You compare it to a critical value from the matching table, or convert it to a p-value: reject H₀ if the statistic is in the rejection region, or equivalently if p ≤ α.
- Type I vs Type II error
- A Type I error rejects a true null hypothesis (probability α, the significance level); a Type II error fails to reject a false null (probability β). Power = 1 − β. Lowering α to guard against false positives raises β unless you also raise n.
- Restricted open-book exam
- The 26134 final format: paper notes, textbook, a calculator of any type and offline Excel/Word/PDF notes are permitted, but the internet and any cloud-stored notes are not. It is ProctorU-invigilated, 120 minutes, 25 equally-weighted questions, with no negative marking.
26134 FAQ
Is 26134 hard?
It is broad rather than deeply mathematical. 26134 spans five modules — descriptive statistics and communication, probability and distributions, sampling and confidence intervals, hypothesis testing, regression and data ethics — so the real challenge is keeping a lot of small methods straight and knowing which one a question wants, not any single hard idea.
Because the restricted open-book exam supplies the Z, t, chi-square and F tables, the marks go to setting up the right formula with correct units, reading the right table, and stating a one-line interpretation. Students who work one example per method each week, rather than cramming the revision week before the formal exam period, tend to find it manageable; steady work also protects your WAM.
First-year students often meet it as a core subject with no statistics prerequisite.
Can AI help me with 26134?
Yes, as a step-by-step study aid. Sia is an AI tutor trained on how 26134 is actually taught and assessed at University of Technology Sydney: it can walk you through standardising a Z-score, building a confidence interval, choosing and running the right hypothesis test from the decision tree, fitting a least-squares line or applying the Five Safes framework, one line at a time, and it checks your reasoning as you go.
Bring your own tutorial or practice question and ask Sia to explain each step. It does not do graded assessment for you — quizzes, the group assignment and the exam are your own work — and the University of Technology Sydney academic-integrity policy still applies. Use it to understand the method, not to produce work you submit.
Where can I find past exam papers / practice for 26134?
Start on Canvas, where the subject posts its exam-preparation material — a full practice exam (the ProctorU practice run), sample questions, and the five statistical tables (Z, t, chi-square, F, binomial) that the exam provides. The UTS Library also holds a past-exam-paper collection; note that older papers may still be labelled "Business Statistics", the subject's former name.
Your tutorial questions and their worked solutions are the closest match to the exam's compute-then-interpret style.
This guide also includes a re-authored practice exam that mirrors the paper's shape — descriptive stats, a probability item, a distribution lookup, a confidence interval, a hypothesis test, a regression read and an ethics scenario — with fresh numbers, and you can ask Sia to generate extra practice in the same style and explain each step. Confirm what is officially provided on Canvas.
What are the 26134 assessment rules and is there a hurdle?
26134 is assessed by six online Canvas quizzes with the best four counting (20% total), a group data-analysis assignment (30% — the standard structure; confirm the current-session weight on the UTS subject outline), and a 120-minute restricted open-book final examination worth 50%.
No pass hurdle or minimum-mark requirement is stated in the subject materials, and UTS applies no negative marking on the exam, but you should confirm the exact weights, any hurdle and the permitted-materials list on your current Canvas Assessments page and the UTS subject outline. The final is invigilated online through ProctorU (a Guardian browser); an on-campus sitting can be requested.
Grades follow the UTS HD / D / C / P scheme, and the UTS academic-integrity policy governs every component.
What is on the 26134 final exam?
One 120-minute restricted open-book paper worth 50% of the subject, delivered online via ProctorU. It has 25 equally-weighted questions presented all at once (you can move back and forth), each a compact compute-then-interpret item spread across all five modules — including Week 2 data communication and Week 11 data ethics, which students sometimes forget are examinable.
You are given the Z, t, chi-square, F and binomial tables and may use a calculator and offline Excel, so the emphasis is applying methods, not memorising formulas. With no negative marking, answer every question. The exam sits in the University of Technology Sydney formal examination period for the Spring session (around November 2026) — confirm the exact date, time and format on Canvas and the UTS exam timetable.
Questions students ask in each 26134 chapter
- When should I report the median instead of the mean?
- Whenever the data are skewed or contain outliers. The mean is dragged toward extreme values, so for right-skewed data like income or salaries the median is the fairer 'typical' figure. Report both if you want to show the skew, and let the mean-vs-median gap signal its direction. Chapter 01 · Exploring Data: Descriptive Statistics
- Why are pie charts often a bad choice?
- Humans compare angles and areas poorly, so it is hard to judge which slice is larger, especially with many similar slices. A bar chart, where length is easy to compare on a common baseline, usually communicates the same categorical data more clearly. Reserve pie charts for a few slices with very different sizes, if at all. Chapter 02 · Communicating Insights from Data
- What is the difference between mutually exclusive and independent?
- They are unrelated ideas. Mutually exclusive means the events cannot happen together (P(A ∩ B) = 0). Independent means one event's occurrence does not change the other's probability (P(A ∩ B) = P(A)·P(B)). In fact two events with non-zero probability that are mutually exclusive cannot be independent, because if one occurs the other's probability drops to 0. Chapter 03 · Predicting Events: Probability Foundations
- When is a variable binomial rather than just discrete?
- It must meet four conditions: a fixed number of trials n, exactly two outcomes per trial (success/failure), the same success probability p on every trial, and independent trials. If p changes between trials or the trials are dependent, it is not binomial even though it is discrete. Chapter 04 · Discrete Outcomes: The Binomial Distribution
- Why is the probability of an exact value zero for a continuous variable?
- Because probability is area under the density curve, and a single point has zero width, hence zero area. So P(X = 25.0) = 0 for a continuous variable; only intervals like P(24.5 < X < 25.5) carry positive probability. This is why continuous questions always ask about ranges. Chapter 05 · Continuous Outcomes: The Normal Distribution
- What is the difference between the standard deviation and the standard error?
- The standard deviation σ describes the spread of individual observations in the population. The standard error σ/√n describes the spread of the SAMPLE MEAN across repeated samples. The SE is smaller by a factor of √n, which is why averaging many observations gives a much more stable estimate. Chapter 06 · Insights from Limited Information: Sampling Distributions
- When do I use t instead of Z for a confidence interval?
- Use Z when the population standard deviation σ is known (rare in practice); use the t-distribution with n − 1 degrees of freedom when σ is unknown and you estimate it with the sample s (the usual case). The t has heavier tails to account for the extra uncertainty from estimating σ, so its intervals are slightly wider. Chapter 07 · Estimating Population Values: Confidence Intervals
- How do I decide between a one-tailed and two-tailed test?
- It comes from the alternative hypothesis. If H₁ is 'differs from' (≠), use a two-tailed test and split α into α/2 in each tail. If H₁ is directional — 'greater than' (>) or 'less than' (<) — use a one-tailed test with all α in that one tail. The claim wording tells you which. Chapter 08 · Testing Ideas I: Hypothesis-Testing Foundations
- How do I tell a paired test from a two-independent-sample test?
- Ask whether each observation in one group is naturally matched to a specific observation in the other. Before-and-after measurements on the same people, or matched pairs, are PAIRED — analyse the differences with a one-sample t-test. Two separate, unrelated groups (e.g. firm A vs firm B) are INDEPENDENT and use the pooled two-sample t-test. Chapter 09 · Testing Ideas II: Comparing Groups
- How do I interpret the slope and intercept?
- The slope b₁ is the estimated change in y for each one-unit increase in x, stated in the variables' units (e.g. '3 more units of sales per extra $1,000 spent'). The intercept b₀ is the predicted y when x = 0; treat it literally only if x = 0 is within or near the observed data, otherwise it is just where the line meets the axis. Chapter 10 · Modelling Relationships: Regression Analysis
- Is data ethics really examinable in a statistics subject?
- Yes. Week 11 is Module 5 and the final exam explicitly spans all five modules, including data communication and data ethics, so a short-answer ethics vignette is fair game. Because it is qualitative, prepare it as a structured framework you can apply, not as content to compute — students who skip it lose easy marks. Chapter 11 · Ethical Use of Data
- What exactly can I bring to the 26134 exam?
- It is restricted open-book: paper notes, the textbook, printed or offline PDF/Word notes, and a calculator of any type are allowed, and the five statistical tables are provided. What is NOT allowed is the internet and any cloud-stored notes (Drive, OneDrive, OneNote). Prepare well-organised printed notes so you can find a formula or table fast. Confirm the current permitted-materials list on Canvas. Chapter 12 · Exam Preparation: The Restricted Open-Book Exam
How to study for the exam
Treat 26134 as a toolbox of about a dozen small methods rather than one long reading, and rehearse one worked example per method every week rather than cramming the revision week before the formal exam period. Build a single decision tree that routes any inference question: one sample or two? A mean, a variance, or a difference? Is σ known (→ Z) or unknown (→ t)? Paired or independent? Two groups (t / F) or more (ANOVA)?
Then drill the table lookups until they are automatic — standardising with the Z-table, t critical values for a CI or a t-test, chi-square for a variance, F for ANOVA and equal-variance tests.
Because the restricted open-book exam supplies all five tables and allows a calculator and offline Excel, practise applying each formula with correct units and a sanity check, not memorising it, and pre-organise your printed notes so you can find the right table and formula fast under the 120-minute clock.
Do not neglect the two modules students under-prepare: Week 2 data communication (truncated axes, pie-chart pitfalls, percentage points vs percent change) and Week 11 data ethics (the four principles, consequentialist vs deontological reasoning, the Five Safes) are both examinable short-answer territory.
With 25 equally-weighted questions and no negative marking, keep pace at roughly one question every four to five minutes, bank the easy computes first, and attempt every question. When a step will not click, ask Sia to explain that single step a different way and set you a fresh practice question in the same style; it teaches the method and checks your reasoning, and it never substitutes for your own graded work.
Confirm the exam date, permitted materials and any assessment changes on Canvas and the UTS subject outline.
Your AI Statistics tutor for 26134
Stuck on a hard 26134 question? Sia is AskSia’s AI Statistics tutor — ask any 26134 Responsible Evidence-Based Decisions 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.
