Uber·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Uber data science interview with a stats-heavy question about comparing proportions across two coins with very different sample sizes. Pretty standard hypothesis testing territory but the sample size imbalance adds a wrinkle that trips people up if they're not careful.

Questions Asked (1)

You have two coins: Coin A flipped 100 times with 40 heads, and Coin B flipped 1000 times with 600 heads. Are the head probabilities statistically different? Walk through your hypotheses, the right test, the test statistic, a 95% confidence interval for the difference, and any caveats around the unequal sample sizes.

A/B Testing & ExperimentationProduct Analytics & Metrics

Author's notes

This is a two-proportion z-test setup and I knew that pretty quickly, but I fumbled the confidence interval formula under pressure.

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AI HintsAI Generated

Suggested Approach

Start by clarifying that this is a two-proportion z-test comparing independent binomial samples. Compute the sample proportions, pooled proportion, standard error, z-statistic, and p-value, then construct a 95% confidence interval for the difference. Finally, discuss how the unequal sample sizes affect power and precision, and mention practical significance.

Pro tip: Emphasize that with large samples, even tiny differences can be statistically significant, so always interpret the effect size and confidence interval in the context of business impact. Also, note that the unequal sample sizes mean the smaller sample (Coin A) contributes more uncertainty to the difference.

1. State hypotheses and assumptions

Define null hypothesis H0: p_A = p_B and alternative H1: p_A ≠ p_B. Check assumptions: independent flips, binary outcomes, and large-sample condition (np and n(1-p) ≥ 10 for both).

2. Compute sample proportions and test statistic

Calculate p̂_A = 40/100 = 0.40, p̂_B = 600/1000 = 0.60. Pooled proportion p̂ = (40+600)/(100+1000) = 640/1100 ≈ 0.5818. Standard error SE = sqrt(p̂(1-p̂)(1/100 + 1/1000)) ≈ sqrt(0.5818*0.4182*0.011) ≈ 0.0517. z = (0.40 - 0.60)/0.0517 ≈ -3.87.

3. Determine p-value and statistical significance

For a two-sided test, p-value = 2 * P(Z < -3.87) ≈ 0.0001. Since p < 0.05, reject H0 and conclude the proportions are statistically different.

4. Construct 95% confidence interval for difference

Use unpooled SE for CI: SE_diff = sqrt(p̂_A(1-p̂_A)/100 + p̂_B(1-p̂_B)/1000) = sqrt(0.24/100 + 0.24/1000) = sqrt(0.0024 + 0.00024) = sqrt(0.00264) ≈ 0.0514. 95% CI: (0.40-0.60) ± 1.96*0.0514 = (-0.20 ± 0.1007) = (-0.3007, -0.0993).

5. Discuss caveats and practical implications

Note that unequal sample sizes affect power and precision; the smaller sample (Coin A) has larger variance. Also, statistical significance does not imply practical significance—consider effect size and business context.

Key Points to Mention

Two-proportion z-test is appropriate for comparing independent binomial proportions.
Check large-sample assumption: np and n(1-p) ≥ 10 for both coins.
Use pooled proportion for hypothesis testing and unpooled for confidence interval.
The difference is statistically significant (p ≈ 0.0001) and the 95% CI excludes zero.
Unequal sample sizes mean the smaller sample contributes more uncertainty; consider power and precision.
Distinguish statistical significance from practical significance; assess effect size in context.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.