Problem 1
z=(82−70)/6=2, so the score is two standard deviations above the mean.
Faculty solution guide
Standard Scores and Relative Standing
Accept equivalent statistically correct reasoning. Require context, design, assumptions, uncertainty, and limits.
Problem 2
A common error is to report a calculation without identifying the population, design, assumptions, uncertainty, context, or limits on causal and generalizing claims.
Problem 3
A complete response identifies population, cases, variables, parameter or estimand, study design, and conditions for Standard Scores and Relative Standing.
Problem 4
Repair the earliest invalid assumption, display, calculation, or inference; then rerun the interpretation and state how the correction changes the claim.
Problem 5
A strong application defines context, data source, design, analysis plan, uncertainty, and limits on generalization or causation.
Problem 6
Use at least two of: independent recomputation, alternative graph or model, residual/diagnostic check, resampling, sensitivity analysis, subgroup analysis, simulation, or comparison with a known benchmark.