Google·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

A Google Data Scientist interview that came down to a single statistics question about hypothesis testing. Pretty focused and short, but the kind of question that trips you up if your fundamentals are rusty.

Questions Asked (1)

You have exactly one numeric observation. How would you test whether it was drawn from a standard normal distribution? Walk through the null and alternative hypotheses and explain how you'd make a decision.

A/B Testing & ExperimentationProduct Analytics & Metrics

Author's notes

Felt weirdly simple at first and that made me second-guess myself.

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AI HintsAI Generated

Suggested Approach

Acknowledge that with a single observation, traditional distribution tests are impossible, so you must reframe the problem as a hypothesis test about the observed value's extremeness under the null. Propose using the probability integral transform or the likelihood under the null to compute a p-value, and discuss the limitations and decision criteria.

Pro tip: Emphasize that with n=1, any test has low power, so the focus should be on quantifying evidence (e.g., p-value) rather than making a definitive decision; also mention that the test is essentially checking if the value is an outlier under the null.

1. Clarify the hypotheses

State the null hypothesis H0: the observation is drawn from a standard normal distribution (mean 0, variance 1). The alternative H1: it is drawn from some other distribution (e.g., normal with different mean/variance, or non-normal).

2. Choose a test statistic

Since there is only one observation, the natural test statistic is the observed value itself (or its absolute value). Under H0, the distribution of this statistic is known: standard normal.

3. Compute the p-value

Calculate the two-sided p-value as 2 * (1 - Φ(|x|)), where Φ is the standard normal CDF. This represents the probability of observing a value as extreme or more extreme than x under H0.

4. Make a decision

Compare the p-value to a pre-specified significance level α (e.g., 0.05). If p-value < α, reject H0; otherwise, fail to reject H0. Note that with n=1, failing to reject does not mean H0 is true.

5. Discuss limitations and alternatives

Acknowledge that this test has very low power and cannot detect many departures from normality. Mention that with only one observation, it's impossible to assess distributional shape; consider Bayesian approaches or additional data if possible.

Key Points to Mention

Null hypothesis: observation ~ N(0,1); alternative: not N(0,1)
Test statistic: the observed value itself; under H0 it follows standard normal
Two-sided p-value calculation using standard normal CDF
Decision rule: reject H0 if p-value < α
Low power and inability to test distributional assumptions with n=1
Alternative approaches: Bayesian posterior predictive check, or collecting more data

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