Investigative Questions and Data Collection — Worked Solutions
Worked Solutions
Compare your reasoning with the worked solutions after attempting the questions. A different valid representation or explanation can earn credit when it satisfies the stated criteria.
Original generated practice for the Fall 2026 course. Return to the lesson and independent checks.
A question has a destination: worked answer
A random sample of current college residents is asked about weekly laundry spending. The study wants a range estimating the mean weekly spending of all current residents.
Part a
Identify the collection variable, the parameter and analysis goal, and the population for the conclusion.
Collect weekly laundry spending in dollars per resident. The parameter is the mean weekly laundry spending of all current residents; the analysis goal is a confidence interval, a plausible range for that mean. The population for the conclusion is all current college residents, not future residents or all college students.
| Evidence for credit | Points |
|---|---|
| Names variable/units and population mean. | 1 |
| Names estimation by a range and correct conclusion population. | 1 |
Every selected item is not every item: worked answer
A club has 180 members. Every one of 30 selected members answers its questionnaire.
Part a
Is this a census of the club membership? Explain, then state what would constitute a census.
No. Only 30 of the 180 members supplied information. A census of the membership records information from all 180 members; complete response within a sample does not make the sample the population.
| Evidence for credit | Points |
|---|---|
| Rejects census with population/sample distinction. | 1 |
| States all 180 must be recorded. | 1 |
Factor, level, or response?: worked answer
A researcher assigns 48 seedlings to either ordinary or nutrient-rich soil and either 6 or 10 hours of light each day. After four weeks, each seedling’s height is measured.
Part a
Identify experimental units, both factors and their levels, all treatments, and the response. State why this is an experiment.
Units are seedlings. Factors are soil type (ordinary, nutrient-rich) and daily light duration (6,10 hours). The four treatments are ordinary/6, ordinary/10, nutrient-rich/6, nutrient-rich/10. Response is seedling height after four weeks. Conditions are imposed by the researcher, so the study is an experiment.
| Evidence for credit | Points |
|---|---|
| Units and experiment mechanism. | 1 |
| Both factors/levels and all four combinations. | 1 |
| Post-treatment height response. | 1 |
Past or future records?: worked answer
Study P selects drivers today, records current mileage, and tracks mileage for six months. Study R selects drivers today and obtains their previous six months of mileage logs. Neither assigns driving habits.
Part a
Identify both study types, explain their time direction, and say whether either is an experiment.
P is prospective: drivers are selected now and data are collected now and into the future. R is retrospective: selected drivers’ past data are gathered. Both are observational because driving habits are not imposed, so neither is an experiment.
| Evidence for credit | Points |
|---|---|
| Correct prospective and retrospective identities with time explanation. | 1 |
| Observational rather than experiment based on no imposed treatment. | 1 |
Two connections are needed: worked answer
A standard-question survey finds that adults who own bicycles report better fitness. Age is associated with both bicycle ownership and fitness. Shirt colour is recorded but is not associated with either.
Part a
Identify the survey as a study type and identify the plausible confounder. Explain both associations and why the result does not establish that bicycle ownership caused better fitness.
The survey is observational, collecting human data with standard questions without assigning bicycle ownership. Age is a plausible confounder because it is related to both ownership and fitness and supplies an alternative explanation of their relationship. Recorded shirt colour is not a confounder here. The observational association therefore does not establish a causal ownership effect.
| Evidence for credit | Points |
|---|---|
| Identifies standardized human survey without imposed treatment. | 1 |
| Age linked to both variables and alternative explanation. | 1 |
| Rejects causal inference and irrelevant recorded-variable claim. | 1 |
Chance in two different places: worked answer
Study A uses a random-number generator to select 60 residents from a complete city roster and asks about their sleep. Study B recruits 60 volunteers and randomly assigns them to one of two bedtime routines.
Part a
Explain which design supports a description of the city population and which supports a cause-and-effect treatment comparison. State the generalization limit for B.
A uses random selection from the city population, supporting population descriptions of sleep, but it did not impose routines and does not support a causal routine claim. B uses random assignment, supporting a comparison of routine effects under the experiment’s conditions. Its volunteer recruitment does not justify generalization to the entire city; scope is participants or similar individuals.
| Evidence for credit | Points |
|---|---|
| Identifies chance selection and population inference in A. | 1 |
| Identifies random assignment and treatment comparison in B. | 1 |
| Correct observational and volunteer-generalization limits. | 1 |
Plan and interpret a transport investigation: worked answer
Urbanopolis has a complete roster of 2,400 current students. A team can either (Plan S) randomly select 120 students with a random-number generator and ask every selected student the same questions about usual trip minutes, travel mode, and lateness, or (Plan V) invite volunteers from a cycling club. A separate teaching experiment recruits 80 volunteer students and randomly assigns a practice game or flashcards, each for either 10 or 20 minutes, then measures words recalled one week later. No transport method is assigned in S or V.
Part a
For Plan S, determine the collection variables and explain the population and types of conclusions the design can support.
Collect usual trip time in minutes, mode category, and late/not-late status for each selected student. Random selection supports generalizations about current Urbanopolis students if collection is sound. Because transport modes are not assigned, mode-versus-time or mode-versus-lateness relationships are observational and cannot establish a causal mode effect.
| Evidence for credit | Points |
|---|---|
| Names all three measured variables. | 1 |
| Identifies current-student population and random-selection basis. | 1 |
| States observational association rather than causal mode effect. | 1 |
Part b
Determine five analysis questions: mean trip time not equal to 20 minutes; mean greater than 20; proportion late less than 0.10; mode and lateness associated/not independent; and a range estimating the mean. Identify the parameter(s) and direction or goal in each.
Questions can be: Is the population mean trip time different from 20 minutes? Is that mean greater than 20? Is the population proportion arriving late below 0.10? Are mode and lateness associated, meaning not independent, among current students? What range plausibly estimates the population mean trip time? The first two concern the population mean with not-equal and greater alternatives; the third concerns the late proportion with a less alternative; the fourth concerns population categorical association/departure from independence; the fifth estimates the population mean with a confidence interval.
| Evidence for credit | Points |
|---|---|
| All three numerical directional alternatives with proper population parameters. | 1 |
| Association and not-independence are linked for categorical variables. | 1 |
| Range-estimation question identifies mean and confidence-interval goal. | 1 |
Part c
Identify whether S is a census, survey, experiment, or observational study; categories may overlap. Explain what change would make it a census of current students.
S is a sample survey and observational study: standard questions collect human data without imposing transport treatments. It is not an experiment and not a census of 2,400 students. Recording information from all 2,400 current students would make it a census.
| Evidence for credit | Points |
|---|---|
| Survey and observational classification with definition. | 1 |
| Rejects experiment/census and identifies complete-population change. | 1 |
Part d
Identify every experimental component in the teaching study: units, subject/participant terminology, factors, levels, four treatments, and response. Explain the timing of the response.
Each volunteer student is an experimental unit, also a subject or participant. Factors are practice method with game/flashcards levels and duration with 10/20-minute levels. Treatments are game/10, game/20, flashcards/10, flashcards/20. Words recalled one week later is the response, measured after the assigned practice. The study is experimental because the researcher imposes these combinations.
| Evidence for credit | Points |
|---|---|
| Human units and subject/participant terms. | 1 |
| Both factors/levels and four treatment combinations. | 1 |
| Post-treatment response and imposed-condition rationale. | 1 |
Part e
Propose one prospective and one retrospective observational extension of Plan S. Specify when units are selected and when the data occurred.
Prospective: select students now, record current trips, and track next term’s lateness without assigning travel modes. Retrospective: select current students now and gather their previous term’s lateness and travel logs. Both remain observational because travel conditions are not imposed.
| Evidence for credit | Points |
|---|---|
| Selection now plus current/future data in prospective extension. | 1 |
| Selection now plus past data in retrospective extension. | 1 |
| No imposed travel treatment in either. | 1 |
Part f
Distance from home is associated with both mode and trip time. Identify its role and explain what two relationships make it relevant.
Distance is a plausible confounding variable: farther students tend to use different transport modes and also have longer travel times. These links to both the explanatory variable (mode) and response (time) provide an alternative explanation of a mode-time association, reducing support for a causal mode claim.
| Evidence for credit | Points |
|---|---|
| Identifies confounder and both variable associations. | 1 |
| Explains alternative causal account rather than simply listing a third variable. | 1 |
Part g
Compare generalizations from S, V, and the teaching experiment. Explain the role of random selection and deliberate or voluntary selection.
S samples by chance from the current-student roster and can support population inference to that group. V consists of volunteers from a cycling club and has neither random selection from all students nor support for all-student generalizations; interpretations are limited to participants or similar individuals. The teaching experiment also recruits volunteers, limiting population scope, but random assignment supports treatment-effect comparisons under the study conditions.
| Evidence for credit | Points |
|---|---|
| S chance mechanism and correct population. | 1 |
| V voluntary/nonrandom selection and limited similar-individual scope. | 1 |
| Teaching random assignment distinguished from population selection. | 1 |
Choose analysis components from four new purposes: worked answer
Four teams are planning separate investigations. For each purpose below, determine the population analysis component before any data are collected. No sample result or alternative direction has been prefilled. A correctly defined verbal alternative is acceptable.
Part a
The public book-drop service historically needed an average of 7 minutes per collection. After changing the collection route, the manager wants to find out whether the current average collection time has changed. Identify the unknown population quantity and formulate the alternative corresponding to this decision purpose. Define any symbol you use; do not perform a test.
The parameter is the current population mean collection time μ, in minutes, for the service’s collections under the changed route. The alternative is μ≠7 minutes: the purpose asks about any change, not only an increase or decrease. In words, the current average collection time differs from 7 minutes.
| Evidence for credit | Points |
|---|---|
| Identifies and contextually defines the current population mean collection time. | 1 |
| Formulates a not-equal alternative against 7 minutes and connects both directions to “changed.” | 1 |
Part b
Last year 40% of the city’s eligible residents used the bike-pass service. The coordinator wants to find out whether this year’s adoption exceeds last year’s rate. Identify the unknown population quantity and formulate the alternative corresponding to this decision purpose. Define any symbol you use; do not perform a test.
Let p be the population proportion of eligible city residents who use the bike-pass service this year. The alternative is p>0.40: adoption has increased beyond the previous 40%. A sample percentage is an estimate of p, not the parameter itself.
| Evidence for credit | Points |
|---|---|
| Identifies and contextually defines the current population adoption proportion. | 1 |
| Formulates the greater-than alternative p>0.40 rather than an arbitrary two-sided claim. | 1 |
Part c
A parcel network previously lost 6% of packages. After introducing a new label, the network wants to find out whether its current loss rate is below that previous rate. Identify the unknown population quantity and formulate the alternative corresponding to this decision purpose. Define any symbol you use; do not perform a test.
Let p be the population proportion of packages lost under the current new-label process. The alternative is p<0.06: the current package-loss proportion is below 6%. The relevant quantity is a proportion of packages, not their mean weight or a sample count.
| Evidence for credit | Points |
|---|---|
| Identifies and contextually defines the current population package-loss proportion. | 1 |
| Formulates the less-than alternative p<0.06 with the correct reference and purpose. | 1 |
Part d
A library wants to know whether membership tier (basic or premium) is associated with preferred format (print, audio or digital) among its current members. Identify the population quantities or categorical relationship to be investigated and formulate the alternative in words. Explain what population comparison would depart from independence.
The alternative is that membership tier and preferred format are associated in the population of current library members: they are not independent. Equivalently, the population proportions preferring print/audio/digital are not all the same across the two tiers; at least one conditional format proportion differs. This concerns a population categorical relationship, not an alternative about a mean or necessarily a causal tier effect.
| Evidence for credit | Points |
|---|---|
| Identifies current members and the two categorical variables/population conditional format proportions. | 1 |
| States association or non-independence and explains it as a difference in at least one population conditional format proportion; does not assert causation. | 1 |
Identify a single-factor experiment: worked answer
A shipping cooperative randomly assigns 45 identical test boxes to one of three packing materials: shredded paper, foam pieces or air pouches. Each box receives just one material, is dropped once from 1 metre under the same protocol, and is then inspected. The recorded outcome is its number of damaged items.
Part a
Identify the experimental unit, the single factor, all its levels, every treatment, and the response variable. Explain how the factor levels determine the treatments in this one-factor design.
The experimental unit is one test box. The sole factor is packing material; its three levels are shredded paper, foam pieces and air pouches. Each level is one treatment because this experiment has only that one factor, so there are three treatments, not nine combinations. The response is the number of damaged items in a box after the imposed drop. The fixed drop height is a controlled feature, not a second varied factor.
| Evidence for credit | Points |
|---|---|
| Identifies box as the assigned unit and packing material as the only varied factor. | 1 |
| Lists all three levels and explicitly identifies those same three levels as the treatments in a one-factor experiment. | 1 |
| Identifies the post-drop damaged-item count as the response and distinguishes the fixed drop protocol from a varied factor. | 1 |
Justify the scope of deliberate selection: worked answer
A library has 900 current members. Using its visit records, the manager deliberately chooses the 20 members with the most weekday visits to ask about preferred weekend opening hours. No random selection is used; no invitation to volunteer is issued. All 20 selected members respond.
Part a
Identify the actual sample-selection mechanism. Justify whether the results support generalizing to all 900 members. Explain why obtaining all 20 responses or having a complete roster does not fix the selection issue.
This is a deliberately chosen sample of the most frequent weekday visitors, not a random sample or a volunteer sample. Their responses describe those 20 selected members, and may be useful for understanding similar frequent weekday visitors, but the design does not establish representation of all 900 members. Frequent weekday visitors may have different weekend preferences from infrequent or weekend visitors. Complete response from the selected 20 removes nonresponse within that sample; it does not give the other members a selection chance. A complete roster is a possible sampling frame, not evidence that this selection was random.
| Evidence for credit | Points |
|---|---|
| Identifies deliberate researcher selection rather than random or voluntary selection. | 1 |
| Limits justified population scope and gives a preference-relevant reason the handpicked frequent visitors may differ. | 1 |
| Explains that full response and a complete roster do not supply chance selection or broad representativeness. | 1 |