Calculate 95% Bootstrap Confidence Interval for Order Values
Company: Pinterest
Role: Data Scientist
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Onsite
##### Scenario
An e-commerce firm wants a 95% confidence interval for the average order value but only has a single historical sample of order amounts.
##### Question
Given an array of past order values, write efficient Python code to return the 95% bootstrap confidence interval using 10,000 resamples. Explain your approach and any performance optimizations.
##### Hints
Use vectorized resampling (np.random.choice) and percentile bounds; avoid Python loops.
Quick Answer: This question evaluates a data scientist's competence in statistical inference using bootstrap resampling, proficiency with numerical computing for large sample operations, and attention to performance optimization.
Given a non-empty list of historical order values (floats), compute a two-sided 95% bootstrap confidence interval for the mean using exactly 10,000 resamples with replacement. Use NumPy's Generator-based RNG for reproducibility: numpy.random.default_rng(seed).choice. Return the 2.5th and 97.5th percentile bounds of the bootstrap sample means as a list [low, high], rounded to 6 decimal places. If the list has one unique value, the interval is that value for both bounds.
Constraints
- 1 <= len(order_values) <= 5000
- Order values are finite floats (can be zero or positive)
- Use exactly B = 10,000 bootstrap resamples with replacement
- RNG must be numpy.random.default_rng(seed) for determinism
- Percentile bounds are [2.5, 97.5]
- Return a list of two floats rounded to 6 decimals
Hints
- Use numpy.random.default_rng(seed).choice to generate resamples in a vectorized way.
- Compute means along axis=1 and then np.percentile at [2.5, 97.5].
- To limit memory, generate resamples in batches (e.g., 1000 at a time) while keeping vectorization within each batch.