Choose the Inference Method from the Question and the Design — Solutions and Rubrics
Use these solutions after completing the independent application. The rubrics describe what the requested action must demonstrate; equivalent correct reasoning is welcome.
Original generated practice for the Fall 2026 course. Return to the lesson and independent checks.
Choose a method and defend its target: worked answer
For each case select a method from the response type, design and investigative goal, not from the mere presence of a table or large n. Every SRS is drawn without replacement; separate town/package samples are independent.
| Case | Complete study and goal |
|---|---|
| A | SRS of 200/8,000 residents, 120 favor a park; estimate support |
| B | SRS of 200/8,000 residents, 120 favor; test population support different from .50 |
| C | Independent SRSs 200/8,000 and 180/7,000 residents, 120 and 81 favor; estimate first-minus-second support |
| D | Same independent two-town samples; test equal support proportions |
| E | Independent SRSs of 90 from each of three 5,000-person towns; walk/bus/drive counts 45/30/15,30/30/30,15/30/45; compare distributions |
| F | One SRS of 200/25,000 city residents records dwelling type and park-visit category; smallest expected two-way count 25; test association |
| G | SRS of 40/4,000 devices gives lifetime mean 12, sample SD 2 hours; estimate mean lifetime with unknown sigma |
| H | SRS of 12/2,400 learners’ test scores in points measured before/after; differences 1,2,2,3,3,4,4,5,5,6,6,7; test mean after-minus-before change |
| I | Independent SRSs of 35/10,000 and 40/12,000 packages with sample means 14.2/12.9 and sample SDs 2.1/2.4 days; test mean difference |
Part a
For case A, choose and name the inference procedure, define its parameter(s)/variables and population(s) with units where needed, and explain which response/design/goal features determine the choice. Explain one tempting incompatible method and why it does not fit.
Use a one-sample z-interval for a population proportion. Target p, proportion of all 8,000 residents favoring the park. The response is binary, one population is sampled, and the goal is estimation; a t-interval for a numeric mean does not estimate a binary proportion.
| Evidence for credit | Points |
|---|---|
| Correct procedure from actual response/design/goal. | 1 |
| Complete contextual target and a defensible explanation of incompatible alternative. | 1 |
Part b
For case B, choose and name the inference procedure, define its parameter(s)/variables and population(s) with units where needed, and explain which response/design/goal features determine the choice. Explain one tempting incompatible method and why it does not fit.
Use a one-sample z-test for a population proportion. Target p, population support proportion; H₀:p=.50, Hₐ:p≠.50. Binary response, one population and equality testing call for proportion z, not mean t.
| Evidence for credit | Points |
|---|---|
| Correct procedure from actual response/design/goal. | 1 |
| Complete contextual target and a defensible explanation of incompatible alternative. | 1 |
Part c
For case C, choose and name the inference procedure, define its parameter(s)/variables and population(s) with units where needed, and explain which response/design/goal features determine the choice. Explain one tempting incompatible method and why it does not fit.
Use a two-sample z-interval for a difference in population proportions. Target p₁−p₂, support proportions for first town minus second town. Two independent populations and a binary response with an estimation goal call for a difference interval; pooling a null is not the estimation step.
| Evidence for credit | Points |
|---|---|
| Correct procedure from actual response/design/goal. | 1 |
| Complete contextual target and a defensible explanation of incompatible alternative. | 1 |
Part d
For case D, choose and name the inference procedure, define its parameter(s)/variables and population(s) with units where needed, and explain which response/design/goal features determine the choice. Explain one tempting incompatible method and why it does not fit.
Use a two-sample z-test for a difference in population proportions. Target p₁,p₂, the two town population support proportions under equality. Independent binary samples and equality testing call for a proportion-difference z test, not a paired numerical t test.
| Evidence for credit | Points |
|---|---|
| Correct procedure from actual response/design/goal. | 1 |
| Complete contextual target and a defensible explanation of incompatible alternative. | 1 |
Part e
For case E, choose and name the inference procedure, define its parameter(s)/variables and population(s) with units where needed, and explain which response/design/goal features determine the choice. Explain one tempting incompatible method and why it does not fit.
Use a chi-square homogeneity test. Target one commute-choice categorical variable compared across the three town populations. Multiple independently sampled populations and one categorical distribution call for homogeneity, not one-population independence.
| Evidence for credit | Points |
|---|---|
| Correct procedure from actual response/design/goal. | 1 |
| Complete contextual target and a defensible explanation of incompatible alternative. | 1 |
Part f
For case F, choose and name the inference procedure, define its parameter(s)/variables and population(s) with units where needed, and explain which response/design/goal features determine the choice. Explain one tempting incompatible method and why it does not fit.
Use a chi-square independence test. Target dwelling type and park-visit category, two categorical variables in one city population. One population sample with two categorical variables calls for independence, not homogeneity across separately sampled populations.
| Evidence for credit | Points |
|---|---|
| Correct procedure from actual response/design/goal. | 1 |
| Complete contextual target and a defensible explanation of incompatible alternative. | 1 |
Part g
For case G, choose and name the inference procedure, define its parameter(s)/variables and population(s) with units where needed, and explain which response/design/goal features determine the choice. Explain one tempting incompatible method and why it does not fit.
Use a one-sample t-interval for a population mean. Target μ, mean device lifetime in hours in the population of 4,000 devices; σ unknown. Quantitative lifetimes, one sample, unknown sigma and an estimation goal call for t, not proportion z.
| Evidence for credit | Points |
|---|---|
| Correct procedure from actual response/design/goal. | 1 |
| Complete contextual target and a defensible explanation of incompatible alternative. | 1 |
Part h
For case H, choose and name the inference procedure, define its parameter(s)/variables and population(s) with units where needed, and explain which response/design/goal features determine the choice. Explain one tempting incompatible method and why it does not fit.
Use a one-sample t-test on the paired differences. Target μ_d, population mean after-minus-before learner score change in points. The same learners supply dependent before/after responses; form one sample of ordered differences. Independent two-sample t would ignore pairing.
| Evidence for credit | Points |
|---|---|
| Correct procedure from actual response/design/goal. | 1 |
| Complete contextual target and a defensible explanation of incompatible alternative. | 1 |
Part i
For case I, choose and name the inference procedure, define its parameter(s)/variables and population(s) with units where needed, and explain which response/design/goal features determine the choice. Explain one tempting incompatible method and why it does not fit.
Use a two-sample t-test for independent population means. Target μ₁,μ₂, mean package shelf lives in days for the two brand populations; σs unknown. Quantitative days from independent brand samples and unknown sigma call for two-sample t, not paired t or categorical chi-square.
| Evidence for credit | Points |
|---|---|
| Correct procedure from actual response/design/goal. | 1 |
| Complete contextual target and a defensible explanation of incompatible alternative. | 1 |