Objectives
- Analyze data/sn-hubble.csv.
- integrate lookback time for selected redshifts and compare luminosity-distance definitions
- Report a reproducible result with units, uncertainty, and provenance.
- Test one model assumption rather than presenting a single fitted number.
Materials and setup
Use Python 3 with NumPy, Matplotlib, and the supplied CSV. Record the file name, row count, columns, units, software versions, and the date of analysis. The supplied extracts are compact teaching files derived from named published summaries; they are not new observations.
Input: data/sn-hubble.csv
Computed check: rho_crit = 3H0^2/(8 pi G) = 1.260744e+11 solar masses Mpc^-3.
Procedure
- Inspect the CSV without plotting first. Record missing values, units, and any selection or calibration fields.
- Make a labeled plot of the raw observable and preserve the supplied uncertainty column where present.
- Implement the governing equation from Lectures 03-04; show the intermediate units in a notebook or script.
- Repeat the analysis after the specified perturbation: remove one endpoint, vary a calibration, or compare a second model.
- Write an evidence chain that distinguishes measured inputs, adopted literature values, derived parameters, and model assumptions.
Measurement and analysis record
| Record | Required entry |
|---|---|
| Input provenance | File, source, access/spot-check status, and level 1/2/3 label |
| Primary fit or transformation | Formula, parameter, units, and code reference |
| Uncertainty | Statistical uncertainty plus sensitivity to the prescribed perturbation |
| Validation | Independent recomputation or comparison with a named benchmark |
Compare Simpson integration at 100 and 1000 intervals and report convergence.
Deliverables and assessment
- Notebook or script with a clean rerun path and input filename.
- One labeled figure and one table of fitted or derived values.
- 600-800 word interpretation with uncertainty and one limitation.
- Short provenance statement and bibliography.
100 points: setup/provenance 15, method 25, quantitative result 25, uncertainty/sensitivity 20, figure and scientific communication 15.
Safety and reproducibility
No observing is required. Preserve raw CSVs, do not overwrite supplied data, and use a fixed random seed if a resampling demonstration is added. Any external download must be logged before use.