“This is a restricted open book exam. The following materials and provisions are permitted: All paper-based, i.e. written and printed, materials, including lecture notes, textbook, tutorial exercises, practice exams or your own notes … You are allowed to use Excel, Word and PDF notes.”(Info about the Final Exam, 26134, Spring 2026)
Component
Weight
Format
Online quizzes
20%
Best 4 of 6 count
Group assignment
30%
Data-analysis project
Final examination
50%
Online; 25 questions
Execution: roughly 4–5 minutes per equal-weight question; route first, compute, attach units, interpret, then move. With no negative marking, attempt every question.
1 · Master RouteCh 12 · Fig 12.2
Route before calculating: target → samples/groups → parameter → assumptions.
Prompt
Use
Table
One mean, σ known
Z
Z
One mean, σ unknown
t, df n−1
t
One variance / SD
χ², df n−1
χ²
Two means, matched
paired t on d
t
Two means, independent; equal variances
pooled t
t
Two variances
F = larger/lower
F
Three+ means
one-way ANOVA
F
Table workflowStandardise first; then select the Z, t, χ², F or binomial table. For t and χ² use df=n−1; for pooled t use n₁+n₂−2; for F preserve numerator/denominator df. A two-sided test puts α/2 in each tail. Write statistic, df and tail beside the lookup before comparing. Under equal weighting, bank quick computes, flag slow items, keep a review buffer, and attempt all 25 because there is no negative marking.
2 · Describe FirstCh 1 · final compute
Variable
Valid summary / display
Nominal
counts, proportions, mode; bar
Ordinal
median/ranks; ordered bar
Discrete numerical
mean/median, variance; bars
Continuous
mean/median, s; histogram/boxplot
centre + spreadx̄ = Σxᵢ/n · range = max−min s² = Σ(xᵢ−x̄)²/(n−1) · s = √s² CV = (s/x̄)×100%
Choose centre: symmetric/no severe outliers → mean + s; skew/outliers → median + IQR. CV is unit-free, so compare relative spread across scales.
Right skew: mode < median < mean; report the robust median.
3 · Communicate HonestlyCh 2 · short answer
Data / task
Chart
Trap
Categorical comparison
bar / dot
pie angles hard to rank
One numerical distribution
histogram / boxplot
bars touch in histogram
Two numerical variables
scatterplot
r measures linear association only
r = cov(x,y)/(sₓs_y), −1 ≤ r ≤ 1
Correlation ≠ causation. Inspect the scatterplot: r≈0 can hide a strong curved relation. For bars, the value axis starts at zero. Distinguish percentage points from relative percent: (new−old)/old×100%.
Same 35%→40% values: truncation invents a visual “surge”.
Frequency field
Definition + check
frequency f
class count; Σf=n
relative frequency
f/n; column sums to 1
percentage frequency
100f/n; column sums to 100%
continuous frequency
equal-width bins; touching histogram bars
Report centre with spread: two datasets may share x̄ but differ sharply in s. A responsible statistic states sample or population, centre used, period, units, source and limitations.
Model trapA binomial is only the special case meeting all four conditions; otherwise use the listed PMF rather than forcing Bin(n,p).
6 · Normal + ZCh 5 · table lookup
X ~ N(μ,σ²): continuous, symmetric, mean=median=mode; total density area=1 and P(X=exact value)=0. Empirical check: ≈68%, 95%, 99.7% within 1, 2, 3 SD.
Sketch and shade first; then decide left, right or difference of left tails.
7 · Sampling DistributionCh 6 · mean probability
Parameter μ,σ,p is fixed/unknown; statistic x̄,s,p̂ varies sample to sample. For the sample mean, E(x̄)=μ and:
SE(x̄)=σ/√n Z=(x̄−μ)/(σ/√n) when σ known
CLT: for large n (rule of thumb n≥30), x̄ is approximately normal regardless of population shape; if the population is normal, x̄ is normal for any n. A fourfold n halves SE.
Sample means stay centred at μ and tighten as n rises.
7b · Ethical DecisionCh 11 · vignette
Four principles: respect for persons (consent/autonomy); beneficence (minimise harm, maximise benefit); justice (fair distribution); respect for law and public interest (lawful, transparent, accountable). Consequentialism judges outcomes; deontology judges duties and means.
Safety belongs to the whole access arrangement, not the dataset alone.
Apply every element to the facts. De-identification reduces but does not remove re-identification risk.
8 · Confidence IntervalsCh 7 · core final
generalestimate ± critical value × SE
Situation
CI for μ
σ known
x̄ ± zα/2·σ/√n
σ unknown
x̄ ± tα/2,n−1·s/√n
Common z*: 90% 1.645 · 95% 1.96 · 99% 2.576. Higher confidence → larger critical value → wider CI. Larger n → smaller SE → narrower CI. Student t has heavier tails; as df→∞, t→Z.
Interpret the procedure: 95% of intervals built this way capture μ. Do not assign 95% probability to the fixed μ after this interval is observed.
Margin E = critical value × SE; confidence and precision trade off.
9 · Hypothesis Test EngineCh 8 · every test
State H₀ with equality and H₁ from the claim.
Choose statistic/table; verify assumptions.
Compute SE and standardised statistic.
Find critical value(s) or p-value.
Reject H₀ if p≤α / statistic enters rejection region; otherwise fail to reject.
Conclude in the problem's units and context.
z=(x̄−μ₀)/(σ/√n) t=(x̄−μ₀)/(s/√n), df=n−1
H₁
Tail
Critical allocation
μ≠μ₀
two
α/2 each side
μ>μ₀
right
all α right
μ<μ₀
left
all α left
Errors: Type I = reject true H₀, probability α. Type II = fail to reject false H₀, probability β. Power = 1−β. Lower α raises β unless n rises.
CI build orderIdentify the parameter; decide whether σ is known; set α=1−confidence and use α/2 per side; compute SE; read z* or t* with df=n−1; find E=critical×SE; report x̄±E with bounds, units and the population mean. Higher confidence or greater spread widens the interval; larger n narrows it only at the √n rate. A point estimate alone gives no sampling uncertainty. For σ² or σ, route to χ²: its interval is asymmetric because χ² is right-skewed.
10 · Compare GroupsCh 9 · choose correctly
Same units before/after → paired; separate groups → independent.
SST=SSB+SSW · F=MSB/MSW variance test: F=s₁²/s₂² (larger on top) df=(n₁−1,n₂−1)
ANOVA H₀: all group means equal. Large upper-tail F → at least one differs; it does not say which. Avoid many pairwise t-tests: they inflate overall Type I error.
OLS minimises squared vertical residuals and passes through (x̄,ȳ).
Interpret b₁ as estimated change in y per one-unit x, with units. Treat b₀ cautiously if x=0 is outside the data. R² is explained variation, not causal proof; confounding or reverse causation may drive association.
slope testH₀:β₁=0 vs H₁:β₁≠0 t=b₁/se(b₁), df=n−2
Reject when |t| exceeds the two-tailed critical value or p<α. Then interpret b₁ in x/y units. Significance supports association, not causation; predict only inside the observed x range.
26134
Worked Drills · Traps · Fast Recall
Responsible Evidence-Based Decisions · UTS · Spring 2026
Full guide + ask Sia about 26134
SIDE 2/2 FIVE WORKED METHODS · COMMON LOSSES · RECALL TABLESCOMPUTE → DECIDE → INTERPRETUse the same notation as the question and show every denominator
W1 · Binomial CallsCh 4 worked · 4 marks
Given: 6 independent calls, sale probability p=0.3; X = sales. Find P(X=2), mean and variance.
Fixed n=6, two outcomes, constant p=.3, independent → X~Bin(6,.3).
The exact event is one highlighted bar, not a cumulative area.
Trappˣ belongs to successes; (1−p)ⁿ⁻ˣ to failures. “At least k” = 1−P(X≤k−1).
Recall · DescriptiveCh 1–2
Prompt
Fast response
right skew
mean>median; report median
sample spread
divide squared deviations by n−1
compare scales
CV=s/x̄×100%
bar chart
zero baseline
34%→38.5%
+4.5 percentage points; +13.2% relative
Ethics Vignette OrderCh 11 worked
Persons: original purpose, consent, reasonable expectations.
Benefit + justice: weigh benefit against profiling/re-identification harm; ask who bears each.
Law/public interest: lawful, transparent, accountable; compare outcomes with duties.
Five Safes: projects, people, data, settings, outputs—apply each to the facts.
Marks come from framework-to-fact mapping, not a bare yes/no verdict.
Consequentialist: are net outcomes beneficial? Deontological: are consent, confidentiality and duties respected regardless of benefit?
Five SafesIs the project appropriate? Are people authorised? Can data identify anyone? Is the setting secure? Are outputs safe? Safety is not a property of the dataset alone.
W2 · Normal SalesCh 5 worked · 4 marks
Given: X~N(500,80²). Find (a) P(X>620), (b) P(440<X<620). Use Φ(1.5)=.9332, Φ(.75)=.7734.
620: z=(620−500)/80=1.5.
P(X>620)=1−Φ(1.5)=1−.9332=.0668.
440: z=(440−500)/80=−.75; Φ(−.75)=1−.7734=.2266.
P(440<X<620)=.9332−.2266=.7066.
Middle band uses a difference; upper tail uses 1−Φ(z).
TrapThe Z table gives left area. Sketch the requested region before subtracting.
Recall · ProbabilityCh 3
Question word
Operation
not
complement: 1−P(A)
A or B
add, subtract overlap
A and B
multiply conditional path
A given B
joint ÷ P(B)
independent?
joint = product of marginals
Conditioning changes the denominator to the stated row or column.
Do not merge concepts: mutually exclusive non-zero events cannot be independent. If A occurs, an exclusive B becomes impossible; independence would leave P(B) unchanged.
Normal / sampling clue
Denominator or area
one observation X
standardise with σ
sample mean x̄
standardise with σ/√n
left of cut
Φ(z)
right of cut
1−Φ(z)
between two cuts
Φ(zᵦ)−Φ(zₐ)
Normal sanity checkFor continuous X, P(X=a)=0, so endpoints do not change an interval probability. A z-score counts SDs from μ. The Z table returns left area Φ(z); sketch first, then use a complement or difference. Check against 68–95–99.7%.
Interpret: the 95% interval-building procedure captures the true mean in 95% of repeated samples.
Point estimate in the centre; margin extends equally on both sides.
TrapUnknown σ means t, and a two-sided interval uses α/2 with df=n−1.
CI / Test LinkCh 7–8
Interval / test
Equivalent two-sided decision
95% CI excludes μ₀
reject H₀ at α=.05
95% CI contains μ₀
fail to reject H₀ at α=.05
Both use estimate−null measured in SEs. CI shows plausible parameter values and precision; the test gives a decision at chosen α. Neither statistical significance nor a narrow interval proves practical importance or causation.
Estimating σ with s adds uncertainty, so t critical values are larger.
Confidence
α
z*
90%
.10
1.645
95%
.05
1.96
99%
.01
2.576
Inference target
Reference distribution
mean; σ known
Z
mean; σ unknown
t, df=n−1
one variance / SD
χ², df=n−1; right-skewed, non-negative
Width check: confidence ↑ widens; n ↑ narrows. A more precise interval is narrower, but precision does not repair a biased sample or prove the model assumptions.
Route: two independent means, σ unknown, equal variances → pooled t; df=12+15−2=25. H₀:μ₁=μ₂; H₁:μ₁≠μ₂.
s²p=[11×36+14×25]/25=746/25=29.84.
SE=√[29.84(1/12+1/15)]=√4.476=2.116.
t=(52−48)/2.116=1.89. Since |1.89|<2.060, fail to reject H₀: insufficient evidence of a mean difference at 5%.
The observed t remains inside the non-rejection region.
TrapPaired observations are not two independent samples: calculate dᵢ and run one-sample t on d.
Group-Test RecallCh 9
Clue
Statistic
df
same units twice
t=d̄/(s_d/√n)
n−1
2 separate means
pooled t
n₁+n₂−2
2 variances
s₁²/s₂²
n₁−1,n₂−1
3+ means
MSB/MSW
k−1,N−k
ANOVA / F ReadCh 9 · Fig 9.3
ANOVA and the two-variance F-test use the upper tail.
ANOVA: H₀ says all means are equal; a large F=MSB/MSW means between-group variation dominates within-group noise. Rejection says at least one mean differs, not which. Variance test: put the larger sample variance on top so F≥1 and keep numerator/denominator df in the same order.
Method
Check before computing
paired t
natural one-to-one matching; analyse dᵢ
pooled t
separate groups; equal variances assumed
ANOVA
three or more means; one upper-tail F
F variance test
ratio of two variances; preserve df order
W5 · Regression from SummariesCh 10 worked · 4 marks
Given: advertising x ($000s) vs sales y: x̄=10, ȳ=50, sₓ=4, s_y=15, r=.8. Find line, predict at x=12, state R².
b₁=r(s_y/sₓ)=.8(15/4)=.8×3.75=3.0. Each extra $1,000 advertising is associated with 3 more sales units.
b₀=ȳ−b₁x̄=50−3(10)=20. Thus ŷ=20+3x.
x=12: ŷ=20+3(12)=56 units.
R²=r²=.8²=.64: 64% of sales variation is explained; 36% remains residual.
The line passes through (x̄,ȳ); use this as the intercept check.
TrapThe slope ratio is s_y/sₓ, not sₓ/s_y. Association and high R² do not prove causation.
Interpretation StemsCh 8–10
Output
Write
test rejects
“At α, evidence that [H₁ in context].”
test does not reject
“At α, insufficient evidence that…”
slope b₁
“Each 1-unit x rise is associated with estimated b₁-unit y change.”
R²
“R²×100% of variation in y is explained by the model.”
CI
state bounds, units, parameter and long-run coverage
Never “accept H₀”. Never call p the probability H₀ is true. Never extrapolate the fitted line beyond observed x without warning.
R²=SSR/SST: explained share; the residual y−ŷ remains unexplained.
Regression check
Meaning
Σeᵢ² minimised
least-squares criterion
line through (x̄,ȳ)
intercept arithmetic check
R²=r²
simple regression only
Confounder checkA confounder is related to x and influences y; omission can bias the simple slope. Multiple regression reads b₁ holding measured predictors constant, but still does not prove causation. A causal claim asks what y would be if x changed and all else stayed the same.
13 · Trap MatrixCh 1–10 FAQs
If you see…
Do this
sample variance
divide by n−1
skew/outlier
prefer median + IQR
sample mean probability
use σ/√n, not σ
σ unknown
use t, df=n−1
two-sided claim
split α/2 per tail
p≤α
reject H₀
same subjects twice
paired t on differences
3+ means
ANOVA, not many t-tests
F variance ratio
larger variance on top
r≈0
check scatter for non-linearity
significant slope
do not infer causation
de-identified data
risk reduced, not eliminated
Your decision is observable; the truth of H₀ is not.
15 · Final 20-Second CheckCh 12
Correct method and table? df and tail right?
SE divides by √n? Units carried?
Probability lies 0–1; variance non-negative?
Decision matches p/critical value?
Conclusion names population, parameter and direction?
Every question attempted?
Offline Excel recall
Function named in guide
centre / sample spread
AVERAGE, MEDIAN, STDEV.S, VAR.S
binomial
BINOM.DIST
normal probability / cut
NORM.DIST, NORM.S.DIST, NORM.S.INV
t confidence margin
CONFIDENCE.T
Exam moveRoute → formula → substitution → value → decision → contextual sentence.
Last-pass symptom
Repair
probability outside 0–1
recheck area, complement and arithmetic
variance / SD confused
variance has squared units; SD has original units
exact value for continuous X
probability is 0; use an interval
“accept H₀”
write “fail to reject H₀”
ANOVA rejected
say at least one mean differs, not which
R² treated as causation
state explained variation only
paired rows treated separately
form dᵢ first; test the differences
F-table lookup
keep numerator and denominator df in ratio order
Saved your GPA? Send this to your study group.
Every share helps another student. Sia is free forever — share is how we grow.
Sia is your free desktop study agent. Drop your University of Technology Sydney 26134 slides — Sia builds a sheet tailored to YOUR exam. Better than this library because it knows YOUR materials.
