Scholarship Statistics 93201

Time series, bivariate modelling, inference, experiments, statistical literacy and probability. Real NZ data contexts with graphs, strategy prompts, worked steps and s/o marking.

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Probability distributions · 31

Surf lifesaving rescue call-outsPoisson and normal models: calculation, conditional probability, model fit and assumptionsScholarship
Cook Strait ferry crossing timesTriangular model: probabilities, mean, conditional probability, checking against dataScholarship
Quality checks on honey-jar lidsBinomial acceptance sampling, Poisson approximation, clustering of defectsScholarship
Kiwifruit grading for exportFinding normal parameters from two percentiles, grade proportions, sums of independent normalsScholarship
Landslips on a rural roadPoisson over different time periods, conditional probability given a total, non-constant ratesScholarship
Late buses on a commuter routeBinomial calculation, normal approximation with continuity correction, independence in contextScholarship
Overbooking a tour busBinomial tail probabilities for a decision; choosing n; checking assumptionsScholarship
Selecting a relay teamSums and differences of independent normal variablesScholarship
Scaled scores in a national competitionNormal percentiles and the distribution of a mean of twoScholarship
Three models at a call centreChoosing between binomial, Poisson and normal models; justifying parametersScholarship
Calls to a roadside assistance lineNormal approximation to Poisson; continuity correction; staffing decisionsScholarship
Honey jars from two filling machinesMixtures of normal distributions from two sourcesScholarship
Days with at least one rescueFrom Poisson events to binomial counts of daysScholarship
Filling 1-litre juice bottlesNormal model for quality control: reducing spread vs re-centringScholarship
Germination tests on seed batchesEstimating a binomial p from data; over-dispersionScholarship
Lost property at a libraryFitting a Poisson model and checking fit with expected frequenciesScholarship
Courier delivery windowsChoosing between uniform and triangular models for arrival timesScholarship
Calls to two after-hours helplinesSums of independent Poisson counts; conditional splitScholarship
Daily quality checks on a packing lineControl limits for a defect count; false alarmsScholarship
Hoiho chicks fledged per nestEstimating a binomial p and checking the fit to clustered dataScholarship
Catering for a hui at a maraeChoosing and combining binomial and Poisson models for a totalScholarship
How long will the deck take?Critiquing a triangular model for job duration using past dataScholarship
Insuring an outdoor summer concertExpected value and SD to evaluate event insuranceScholarship
Underweight butter blocks at a dairy factoryDetecting a mean shift with a control chart for sample meansScholarship
Making the Interislander check-inSums of independent normal times; planning departureScholarship
Marathon finishing timesEstimating normal parameters from two percentiles; checking the fit with a thirdScholarship
Train or car from Porirua to WellingtonComparing two normal variables: P(X > Y) and reliabilityScholarship
Biosecurity inspection of shipping containersNormal approximation to the binomial: when it works and when it misleadsScholarship
Bike thefts on a university campusOverdispersion: variance above the mean as evidence against a single Poisson rateScholarship
A 'fish or partial refund' guarantee for a fishing charterExpected cost and variability of two guarantee designsScholarship
Daily rainfall at a Wellington weather stationBounded data with many zeros: normal misfit, two-stage model and clusteringScholarship

Experimental design · 32

Seed coating and mānuka seedling growthUnit of allocation, pseudo-replication, and redesigning an experimentScholarship
Nature walks and stressChoosing a control treatment, change scores, interpreting a one-sided randomisation test, limits of blindingScholarship
Fertiliser and irrigation on a maize trialTwo-factor experiment: main effects, interaction, designScholarship
Homework club and endorsementsSelf-selection in observational data, relative risk, designing an ethical experimentScholarship
Two keyboard layoutsCrossover design: treatment and period effects, carryoverScholarship
Caffeine and reaction time: planning sample sizeHow group size affects the re-randomisation distribution and the evidence from an observed differenceScholarship
A reading programme trialled in five schoolsRandomised block design with schools as blocks; exact sign-flip randomisation testScholarship
Practice-reminder messages for te reo Māori learnersNon-compliance: intention-to-treat vs per-protocol vs complier effectScholarship
Anti-fatigue mats in an apple packhouseControl groups and the Hawthorne effect in workplace trialsScholarship
Fertiliser dose and seedling growthDose–response experiment: fitting a line to part of the range, plateau, extrapolationScholarship
Three study techniquesThree-group experiments and multiple pairwise comparisonsScholarship
A mindfulness programme with a waitlistWaitlist control designs: estimating effects and replicationScholarship
Trialling a school exercise programmeWhen blinding is impossible: objective outcomes and blinded assessorsScholarship
Comparing three keyboard-free typing methodsBalancing order with three treatmentsScholarship
Planning a fertiliser trial for avocadosEffect size, variability and sample size in planning an experimentScholarship
A regional speed-limit changeNatural experiments and difference-in-differencesScholarship
A new literacy programme compared with last year's studentsHistorical controls vs concurrent randomised controlsScholarship
A sun-safety programme randomised by classCluster randomisation: design effect and effective sample sizeScholarship
Study time and background musicTwo-factor experiment with interactionScholarship
Testing a new running shoeChoosing between paired and independent designs using variabilityScholarship
A new wound dressing trialControl choice and ethics: standard care vs placeboScholarship
Two maths programmes in two schoolsComparing methods across ability bands (stratified comparison)Scholarship
Recess activity and afternoon focusInterpreting a non-significant randomisation result with effect sizeScholarship
A pasture growth spray on a Waikato dairy farmUnit of allocation: paddocks, not quadratsScholarship
A new milk replacer for dairy calvesBlocking on birth weight in a calf trialScholarship
A herbal muscle gel for netball playersSeparating the placebo effect from the treatment effectScholarship
Men's sheds and loneliness in older menCan an observational survey show that men's sheds reduce loneliness?Scholarship
A hand-hygiene lesson in a Rotorua schoolContamination between treatment and control groupsScholarship
A falls-prevention exercise programmeDropout and intention-to-treat analysisScholarship
Standing desks in a Tauranga intermediateMany outcomes, chance findings and pre-registrationScholarship
Spending alerts in a credit-union appVolunteers, compliance and generalising a spending-alert trialScholarship
A reading programme rolled out across Northland schoolsStepped-wedge rollout and time trendsScholarship

Probability · 39

Cycling incidents surveyThree-set Venn reconstruction, exposure-adjusted risk, solving for a countScholarship
School gala prize wheelDiscrete random variable: expected value and SD, designing a game, totals over many plays, behavioural assumptionsScholarship
Driving-test pass rates at two centresTwo-way tables with a third variable: Simpson's paradox, relative risk, lurking variablesScholarship
Choosing a student wellbeing panelProbabilities by counting (combinations), conditional probability, simulation variability, judging fairnessScholarship
Extended warranty on an e-bikeExpected value decision with risk, multi-stage probabilitiesScholarship
A goal-kicker's streaksTree diagrams with dependent trials; comparing with an independent (binomial) modelScholarship
Plagiarism detectionConditional probability with two sequential tests; independence of testsScholarship
Catching a legal-size snapperWaiting-time ('first success') probabilities, expected value, assumptionsScholarship
Shared birthdays in a classBirthday problem: complement products, model assumptionsScholarship
Cars per householdDiscrete random variable from a frequency table; totals; open-ended categoriesScholarship
A DNA database matchDatabase searches and the prosecutor's fallacyScholarship
Pooled testing of beehivesPooled testing: expected number of tests, optimal pool size, assumptionsScholarship
Testing soil for kauri diebackPositive predictive value at different prevalencesScholarship
A school fundraiser raffleRaffle expected value; probability of winning with multiple tickets without replacementScholarship
Ferry delays and weatherLaw of total probability and reverse conditioningScholarship
Breakfast and afternoon concentrationTesting independence of two categorical variables from dataScholarship
Collecting all four cereal-box cardsExpected waiting time to collect a full setScholarship
Flood risk for a new houseInterpreting '1-in-100-year' events over long periodsScholarship
A 'lucky seven' gala gameFairness of a dice game: expected value and long-run outcomesScholarship
Two smoke detectors and a false alarm problemCombining evidence from two independent alarmsScholarship
Simulating a school's sports drawSimulation design to estimate a probabilityScholarship
Student activities surveyThree-set Venn diagrams; conditional probability; independenceScholarship
Car insurance excess choiceExpected value with an insurance excess; choosing a policyScholarship
How good is the rain forecast?Evaluating a forecaster with conditional probabilitiesScholarship
Sunscreen use and sunburnRelative risk and a CI for a difference in proportions from observational dataScholarship
A netball team's winning streakStreaks under independence: how often do 'hot streaks' occur by chance?Scholarship
A three-prize school raffleWithout-replacement probabilities in a raffle; expected prizesScholarship
Helmets and head injuries at a ski-field medical centreRelative risk, odds and confounding in a three-way tableScholarship
Household emergency preparednessReconstructing a three-set Venn diagram from survey countsScholarship
Two-stage TB testing of cattleSequential testing: tree diagrams, expected counts and the independence assumptionScholarship
Choosing dogs for a shelter's promo shootFinding an unknown total from a 'two chosen' probability (quadratic)Scholarship
Beach drownings and swimming abilityBase-rate reasoning and per-exposure rates in a news claimScholarship
Recruiting colour-blind students for a vision studyExpected counts, simulation design and checking a binomial modelScholarship
Screening and confirming tests in sport drug testingBayes' reasoning with two pieces of evidenceScholarship
Testing a kiwifruit block for a bacterial disease before sprayingExpected cost of a decision with an imperfect testScholarship
Seatbelt use and deaths in rural and urban crashesRisk ratio versus risk difference across subgroupsScholarship
Risk-targeted roadside inspections of heavy trucksExpected waits and targeted inspectionScholarship
An office Secret Santa drawMatching problems and simulationScholarship
Probability of an Alpine Fault earthquakeConstant-rate versus renewal models for rare eventsScholarship

Statistical literacy · 38

Food-delivery app survey reportEvaluating claims in a survey report: CIs, ratio claims, rule-of-thumb limits, causation, non-sampling errorScholarship
Council water-use surveyNon-response bias, weighting by known proportions, within/between MOE comparisonsScholarship
Maths app trial for Year 9 studentsEvaluating an RCT report: CI for a difference, differential drop-out, contaminationScholarship
Bus commuting claimsPercentage vs percentage-point change, misleading graphs, comparing census figuresScholarship
Smoke alarms and house-fire deathsAbsolute vs relative risk reduction, number needed, confounding in observational risk dataScholarship
Choosing a site for a new town poolWithin-group comparisons, undecided respondents, changing the baseScholarship
A study that tested twenty outcomesMultiple comparisons, false positives, evaluating a research claimScholarship
Road deaths in two regionsChoosing denominators: per capita vs per distance; rankings that reverseScholarship
Cafés and registered dogsSpurious correlation between trending time series; detrendingScholarship
Support for a new rates structure by ageWeighting by age group; quota vs random samplesScholarship
Three statistical claims in a magazineDoubling of small risks; percentages of percentages; mean vs medianScholarship
Night-shift work and injuries: reading a research summaryInterpreting a CI for a relative risk in a research summaryScholarship
Do Kiwis sleep less than Australians?Interpreting small but 'significant' differences in national comparisonsScholarship
Do university dropouts make better entrepreneurs?Survivorship bias; comparing success rates in full populationsScholarship
Average class size vs students' experienceAverages from different perspectives: class size paradoxScholarship
Sale prices and 'half-off' claimsSuccessive percentage changes and percentage-of-percentage errorsScholarship
Has membership grown or shrunk?Cherry-picked time windowsScholarship
Why a poll's MOE is larger than 1/√nDesign effects from weighting in published pollsScholarship
Checking expense claims with first digitsBenford's law as a screening tool for invented dataScholarship
Private tutoring hours and exam marksDose–response in observational data: strengthens but doesn't prove causationScholarship
A survey on a four-day working weekEvaluating three claims from a survey: overall, between groups, small subgroupScholarship
'Most crashes happen close to home'Exposure and base rates: crashes near homeScholarship
A dual-axis graph of café openings and coffee pricesDual-axis graphs that suggest false relationshipsScholarship
Estimating how many students have cheatedRandomised response for sensitive questionsScholarship
Three polls in the same weekCombining polls; house effectsScholarship
A small trial of a reading-glasses appAbsence of evidence is not evidence of absenceScholarship
A sitting-time survey in the newsNon-sampling errors and their direction in a media survey reportScholarship
Lowering the voting age in local electionsCIs for differences between and within groups in a pollScholarship
How many New Zealanders still use cash?Coverage error of an online panelScholarship
A flyer about health-line hold timesA truncated bar graph that compares different seasonsScholarship
Does learning an instrument boost maths results?A causal press release: confounding by household incomeScholarship
Are farm waterways fenced off from stock?Bounding and correcting non-response bias with a follow-up sampleScholarship
A council survey on water-meter chargesNon-response bias: bounds and a follow-up sampleScholarship
Checking a post-election survey against the electoral rollSocial desirability bias in self-reported votingScholarship
Red-light cameras at top-ten crash intersectionsCrash 'blackspot' league tables and regression to the meanScholarship
Reminder-letter wording and bowel screening uptakeStatistical vs practical importance in a very large trialScholarship
Gardening and dementia in older New ZealandersAn expert's causal claim from a cohort studyScholarship
How many households have contents insurance?Sampling vs non-sampling error budgetScholarship

Time series · 20

Monthly milk-solids collectionDecomposition with a centred moving average: seasonal adjustment, forecasting, model critiqueScholarship
Forecasting international visitor arrivalsInterpreting forecast intervals, widening uncertainty, judging an actual valueScholarship
Has the price of a pie really gone up?Price index: annual changes, average growth, real vs nominal changeScholarship
Ice-block sales at a dairy chainMultiplicative seasonal indices: seasonally adjusting and forecastingScholarship
Growth in visitor numbersLinear vs compound growth models, forecasting, structural breaksScholarship
Unusual months in hydro-lake inflowsResidual analysis: identifying unusual values relative to residual spreadScholarship
Holt–Winters vs a naive seasonal forecastComparing forecasting methods with mean absolute errorScholarship
Population growth in two districtsIndex numbers for growth comparisons; absolute vs relative growthScholarship
Rainfall and next month's river flowLagged relationships between time series; forecasting with a lead indicatorScholarship
Bus patronage after a fare cutDetecting a change after an intervention; comparing means of periodsScholarship
Easter and quarterly accommodation dataCalendar effects (moving holidays) in quarterly dataScholarship
Smoothing weekly café salesChoosing a moving-average length: smoothing vs responsivenessScholarship
Seasonality of visitor spending in two regionsComparing seasonal indices between regions (multiplicative)Scholarship
Projecting school roll growthUncertainty in growth-rate projectionsScholarship
Seasonally adjusted retail salesSeasonally adjusted series: quarterly growth and annualised ratesScholarship
Quarterly visitor spending at a ski fieldAdditive vs multiplicative decomposition: diagnosing from residuals and swingsScholarship
Quarterly merino thermal salesInterpreting Holt-Winters output: components, forecasts and intervalsScholarship
Missed hospital appointments after text remindersA structural break: estimating an intervention effect against a trend and a comparison seriesScholarship
Quarterly new-dwelling consents in CanterburyJudging Holt–Winters forecasts against what actually happenedScholarship
Quarterly sales at a Hawke's Bay cellar doorMultiplicative seasonal indices: deseasonalising, comparing quarters and forecastingScholarship

Bivariate data and modelling · 25

Dissolved oxygen in two stream catchmentsComparing two fitted models, residuals relative to scatter, classification, extrapolationScholarship
Used-car prices and ageLinear vs exponential models: residual patterns, predictions, interpreting a growth/decay rateScholarship
GPs per head and life expectancyRegional (aggregate) data, ecological fallacy, confoundingScholarship
Body mass and metabolic rate of native birdsLog–log (power) models: interpretation, prediction, back-transformationScholarship
Vineyard area and grape harvestNon-constant scatter: effect on prediction accuracy and remediesScholarship
House prices by floor area in two suburbsComparing regression lines for two groups; crossover point; interactionScholarship
A catch-up programme that 'works'Regression to the mean in test–retest data; evaluating an interventionScholarship
Kūmara yield and rainfallPrediction ranges for individuals vs means; extrapolationScholarship
Weight gain of lambs on two pasturesComparing growth rates of two groups with separate regression linesScholarship
Caffeine in the bloodstreamExponential decay via a log-linear model; half-lifeScholarship
Fish length and mercury levelInfluential points: effect on slope, r and classification decisionsScholarship
Daily ice-cream sales and temperatureResiduals in time order: autocorrelation and missing time effectsScholarship
Nitrogen fertiliser and wheat yieldQuadratic dose–response: optimum, interpolation, economicsScholarship
Kayak hires and temperature at two Abel Tasman basesComparing two regression lines (different slopes)Scholarship
A recovering skink populationExponential growth via a log-linear model; doubling time; limitsScholarship
Do NCEA results predict university grades?Restriction of range weakens correlationsScholarship
Rainfall and pasture growthBootstrap CI for a slope; precision of a relationshipScholarship
Fuel use of a harbour ferryChoosing between linear, exponential and power models from outputScholarship
Class size and maths resultsA lurking variable reverses the slope: subgroup regression linesScholarship
Which blueberry variety is this?Classifying an unknown using two regression modelsScholarship
Predicting marathon times from half-marathon timesPrediction intervals in words, and r versus r²Scholarship
Wind speed and turbine power outputA high r with a curved residual patternScholarship
The spread of wilding conifers in a high-country regionInterpreting a log-transformed modelScholarship
Air temperature and altitude on either side of the Southern AlpsInterpreting an interaction term in supplied regression outputScholarship
Cycleways and city-centre retail spendingTime as a lurking variableScholarship

Statistical inference · 30

Paid work hours of Year 13 studentsBootstrap CI for difference in means: effect of an outlier, cluster sampling, defining groupsScholarship
Counting kererū in a forest reserveEstimating a population total from plots, bootstrap CI, detection error, stratified samplingScholarship
School start times and sleepInterpreting a CI that contains 0, correcting misconceptions, sample size planningScholarship
Life jacket use by kayakersComparing rule-of-thumb, formula and bootstrap intervals for a proportion; non-sampling issuesScholarship
Snapper lengths in two harboursInformal inference from box plots (DBM/OVS) vs bootstrap; sampling issuesScholarship
An online student survey with low responseBounding the effect of non-response; MOE vs biasScholarship
Hi-vis use: e-bike vs conventional commutersCI for a difference in proportions: rule of thumb vs bootstrap; sampling issuesScholarship
Bird counts before and after predator trappingPaired vs independent analysis of before/after dataScholarship
Choosing a confidence level for a pollConfidence level vs width; formula intervals; choosing a levelScholarship
Estimating trout numbers in a lakeCapture–recapture estimation, assumptions and sensitivityScholarship
Days to sell a houseBootstrap CIs for mean vs median with skewed data; asymmetric intervalsScholarship
Has support for a four-day school week changed?Comparing two independent surveys over time; changing MOEs; claims about trendsScholarship
Sleep and reaction timeBootstrap CI for a correlation coefficient; sample size effectScholarship
A huge survey finds a tiny differenceStatistical vs practical significance with very large samplesScholarship
Wait times at two emergency departmentsBootstrap CI for a difference in medians with unequal spreadsScholarship
A school-leaver destination surveyResponse rates and representativeness; comparing respondents with known population figuresScholarship
Preferred new team uniformWithin-group comparisons among three options; 2 × MOEScholarship
Do overlapping intervals mean no difference?Overlapping confidence intervals vs a CI for the differenceScholarship
Surveying most of a small schoolFinite population correction when sampling a large fractionScholarship
Knowing where the nearest defibrillator isBootstrap CI for a difference in proportions; rule-of-thumb comparison; sampling designScholarship
A regional youth wellbeing surveyPlanning sample sizes for subgroup estimatesScholarship
How many students have had a sports concussion?CIs for small proportions: rule of thumb vs formulaScholarship
Consistency of two bus routesComparing spread: bootstrap CI for a difference in IQRsScholarship
Car-share pods and household drivingBootstrap CI for a difference in medians: relative effect and causal limitsScholarship
A district council survey of freedom campersMOE rules for a survey, comparing groups, and critiquing a sampling planScholarship
Building consent processing times in two councilsComparing two councils with bootstrap and proportion intervalsScholarship
Weekly cycling in two citiesBootstrap interval for a difference in proportionsScholarship
A Kāpiti Coast survey on dog-exercise beach rulesChoosing a sample size for subgroup estimatesScholarship
First-timers on the Tongariro Alpine CrossingWhat claim can a non-random sample support?Scholarship
Processing times for student allowance applicationsBootstrap CI for a difference in means, precision and causationScholarship

Statistical investigation · 15

Weekly rents in two regionsMultivariable comparison, derived variables, composition effectsScholarship
Cleaning student height dataData cleaning decisions, effect on mean and median, documenting choicesScholarship
Part-time work and NCEA creditsPlanning a full PPDAC investigation with ethics, sampling and confoundingScholarship
Kiwi chick survival and predator controlMultivariable comparison of rates; interaction; observational limitsScholarship
A district survey on library servicesDesigning a survey: invitations from response rates, stratified allocation, non-responseScholarship
Smart water meters and leak alertsDesigning a detection rule from sensor data: false alarms, sensitivity, assumptionsScholarship
Walking to school by school levelExpected counts under no association; comparing observed with expected; investigating a relationshipScholarship
Earthquake counts by magnitudeLog-linear relationships in count data (Gutenberg–Richter); prediction and limitsScholarship
Time spent gaming on a school nightZero-inflated data: choosing summary statistics and reporting two-part summariesScholarship
Late-night noise complaints in two townsComparing groups of different sizes: relative frequencies, relative risk, display choiceScholarship
Speeding outside a schoolPlanning an observational speed survey; proportions and appropriate MOEScholarship
Random rounding in small-area statisticsConfidentiality rounding in official data; effect on small-area ratesScholarship
Café sales by weather and day typeTwo-factor observational data: main effects and interaction in contextScholarship
Planning a commute-time surveySample size from a pilot SD; practical constraintsScholarship
Two teachers marking the same essaysMeasurement reliability: agreement between raters beyond chanceScholarship