Databricks·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Databricks data scientist interview with a statistics-heavy question on hypothesis testing. Pretty straightforward if you've done any stats work, but the level of rigor they expected was higher than I anticipated.

Questions Asked (1)

You flip a coin 1000 times and observe 560 tails. At a 0.05 significance level, test whether the coin is fair. Walk through your hypotheses, test statistic, p-value calculation, and conclusion.

A/B Testing & ExperimentationProduct Analytics & Metrics

Author's notes

I knew this was a two-sided z-test for a proportion but I fumbled the variance formula for a second.

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AI HintsAI Generated

Suggested Approach

Start by clearly stating the null and alternative hypotheses, then compute the z-test statistic for a proportion using the normal approximation to the binomial. Calculate the two-sided p-value, compare it to the 0.05 significance level, and conclude whether the coin is fair, while noting any assumptions and practical implications.

Pro tip: Mention that with 1000 flips, the normal approximation is valid, and briefly discuss the effect size (560 vs 500) to show you understand both statistical and practical significance.

1. State hypotheses

Define the null hypothesis (H0: p = 0.5, the coin is fair) and the alternative hypothesis (Ha: p ≠ 0.5, the coin is not fair). Specify that this is a two-sided test.

2. Check assumptions and compute test statistic

Verify that np0 ≥ 10 and n(1-p0) ≥ 10 to use the normal approximation. Calculate the z-statistic: z = (p_hat - p0) / sqrt(p0(1-p0)/n), where p_hat = 560/1000 = 0.56.

3. Calculate p-value

Find the two-sided p-value using the standard normal distribution: p-value = 2 * P(Z > |z|). For z ≈ 3.79, the p-value is approximately 0.00015.

4. Compare and conclude

Compare the p-value to the significance level α = 0.05. Since p-value < 0.05, reject the null hypothesis. Conclude that there is sufficient evidence to suggest the coin is not fair.

5. Discuss practical significance and limitations

Note that the observed proportion (0.56) is 12 percentage points away from 0.5, which may be practically significant. Mention that the test assumes independent flips and a fair comparison, and consider confidence intervals for the true proportion.

Key Points to Mention

Null and alternative hypotheses (H0: p=0.5 vs Ha: p≠0.5)
Test statistic formula for a proportion and its calculation (z ≈ 3.79)
Two-sided p-value calculation and interpretation (p ≈ 0.00015)
Comparison to significance level (α=0.05) and decision to reject H0
Assumptions: independence, large sample size for normal approximation
Practical significance: effect size and confidence interval for p

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