Top 30 Statistics Interview Questions and Answers
30 multiple-choice questions on Statistics, drawn from 30 bites out of the 196 tagged Statistics on Tezvyn. Answer them here or read straight down. Every question carries the correct option, why it is correct, and a link to the bite it came from.
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Question 1 of 30
Which statement best describes the fundamental way regularization helps a model avoid overfitting?
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Answer: b · It encourages the model to learn smaller, less extreme parameter values.
Regularization adds a penalty to the loss function for large parameter values, which encourages the model to learn simpler, less extreme weights, thus preventing it from memorizing noise. Option A describes a beneficial outcome of regularization, but not its direct mechanism; it doesn't explicitly "ignore" data points but rather reduces their influence by constraining parameter magnitudes.
Read the full bite: Regularization: Penalizing Complexity to Prevent Overfitting
Question 2 of 30
A checkout A/B test shows significantly higher conversion but slightly lower AOV. What is the strongest basis for a launch recommendation?
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Answer: d · Estimate net revenue and ensure the AOV decline is within a pre-specified non-inferiority margin
The right framework classifies conversion as a success metric and AOV as a guardrail requiring non-inferiority, then uses net revenue to judge the business outcome. Treating AOV as a co-success metric that must significantly increase is a tempting error that causes unnecessary conservatism and missed wins.
Read the full bite: How would you recommend launching a checkout flow with mixed A/B metrics?
Question 3 of 30
Which core concept allows causal inference to distinguish cause-and-effect from mere association?
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Answer: c · The estimation of a counterfactual outcome
The card explicitly states that causal inference's mental model is to create a 'counterfactual'—what would have happened if the cause had not been introduced—to determine the causal effect. While identifying confounders and using RCTs are crucial methods in causal inference, the counterfactual is the underlying conceptual tool for distinguishing causation from association. Analyzing correlations is what causal inference aims to move beyond.
Read the full bite: Causal Inference: Proving Cause, Not Just Correlation
Question 4 of 30
Which hypothesis pair best tests whether a green signup button increases registrations compared to blue?
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Answer: b · H0: The registration conversion rate for green equals that for blue; H1: The registration conversion rate for green is strictly greater than that for blue.
The correct answer frames H0 as no difference and H1 as a directional increase in the specific metric, matching the one-tailed nature of the business question. Option A is tempting because it uses 'no difference,' but it wrongly uses a two-tailed alternative that ignores the directional ask and wastes statistical power.
Read the full bite: What are your null and alternative hypotheses for this A/B test?
Question 5 of 30
You run an experiment and obtain p = 0.03. Which statement correctly interprets this p-value?
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Answer: c · If the null hypothesis were true, there is a 3% probability of observing data at least this extreme.
A p-value assumes the null hypothesis is true and quantifies the probability of seeing data at least this extreme under that assumption; it does not measure the probability that the null is false, that the alternative is true, or that the result occurred by chance.
Read the full bite: What is a p-value? Interpret p = 0.03 at alpha = 0.05.
Question 6 of 30
Which statement accurately describes a key characteristic of a probability distribution?
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Answer: b · It maps every possible outcome of a random process to its specific probability.
A probability distribution is defined as a map of all possible outcomes and their chances, assigning a probability to each. It does not always follow a bell curve, and its purpose is to quantify uncertainty, not to predict exact outcomes or analyze deterministic processes.
Read the full bite: Probability Distributions: Mapping Odds to Outcomes
Question 7 of 30
What justifies using a z-test for a population mean when the underlying data are heavily skewed?
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Answer: a · The sampling distribution of the sample mean becomes approximately normal for large n
The CLT states that the sampling distribution of the sample mean approaches normality as n grows, which justifies using z-tests even when the population is skewed. Option B describes the Law of Large Numbers, a common look-alike that explains convergence to a single value rather than the bell-curve shape required for inference.
Read the full bite: Explain the Central Limit Theorem and its importance for hypothesis testing
Question 8 of 30
When a medical test is 99% accurate, why does Bayes' Theorem suggest a positive result might not mean a 99% chance of having the disease?
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Answer: a · The base rate, or initial prevalence of the disease in the population, significantly impacts the true probability.
The card emphasizes that Bayes' Theorem corrects intuition by incorporating the base rate (prior probability) of the disease. A low base rate means even a highly accurate test can yield many false positives, making the posterior probability of having the disease much lower than the test's accuracy suggests. Option D is tempting but incomplete, as it doesn't explain *why* the 1% error is so impactful in this context, which is due to the base rate.
Read the full bite: Bayes' Theorem: Updating Beliefs with Evidence
Question 9 of 30
Which scenario represents an inappropriate application for linear regression?
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Answer: d · Predicting whether a customer will churn (yes/no) based on their service usage.
Linear regression is designed to predict continuous numerical values, not categorical outcomes like 'yes/no' for customer churn. The other options involve predicting continuous numerical values, which is the primary purpose of linear regression.
Read the full bite: Linear Regression: Finding the Line of Best Fit
Question 10 of 30
In a hypothesis test with an alpha of 0.05, what is the correct interpretation if your p-value is 0.03?
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Answer: c · You have sufficient evidence to reject the null hypothesis.
The card states that if the p-value is less than alpha (p < alpha), you 'reject the null hypothesis.' Since 0.03 is less than 0.05, the null hypothesis is rejected. The p-value is not the probability of the null hypothesis being true, which is a common misconception.
Read the full bite: Hypothesis Testing: A Courtroom for Your Data
Question 11 of 30
In a two-proportion conversion test, which change most directly explains why detecting a 2% relative lift requires roughly 390k users per variant instead of 63k for a 5% relative lift?
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Answer: a · The absolute MDE shrinks from 0.5 to 0.2 percentage points, and sample size scales roughly with the inverse square of the absolute effect size.
The correct answer identifies that the absolute MDE falls from 0.5 to 0.2 percentage points, and because N is roughly proportional to the inverse square of the absolute MDE, required sample size balloons by about sixfold. Distractor D is tempting because it quotes the true p(1-p) variance formula from the card, but in this range variance barely changes and cannot explain the explosion in sample size.
Read the full bite: How do you determine sample size for a conversion lift experiment?
Question 12 of 30
Under what condition does MAP estimation give essentially the same result as MLE?
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Answer: a · When the prior is uniform or the dataset is very large
A uniform prior makes the posterior proportional to the likelihood, and with large data the likelihood overwhelms any prior, so MAP converges to MLE. A strong prior on small data does the opposite.
Read the full bite: MLE versus MAP estimation and the role of priors
Question 13 of 30
An engineer fits a distribution to server latency using MLE and reports tight confidence intervals. If the chosen distribution family does not match the true data-generating process, what best describes the result?
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Answer: b · The estimates maximize likelihood within the wrong family and can be precisely misleading
C is correct because MLE finds the parameters that make the observed data most probable within the assumed model, so a wrong family yields a precise but misleading fit. D is tempting but wrong because misspecification does not automatically inflate uncertainty; the method can be confidently wrong.
Read the full bite: MLE: Find the Parameters That Make Data Likely
Question 14 of 30
For which scenario would a UX researcher most appropriately choose probability sampling over convenience sampling?
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Answer: c · To make a high-stakes strategic decision requiring findings generalizable to an entire user base.
Probability sampling is essential for high-stakes strategic decisions where findings must be generalizable to a broader population. Options A, B, and D describe situations where convenience sampling is recommended due to its speed and cost-effectiveness for identifying usability issues or getting quick feedback.
Read the full bite: UX Sampling: Convenience vs. Probability
Question 15 of 30
When encountering 10% nulls in a key numerical column, what is the most critical first action before choosing an imputation method?
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Answer: b · Investigate the root cause and characteristics of the null values.
The card emphasizes diagnosing the problem before prescribing a solution. Understanding the root cause and characteristics of nulls is crucial to determine the most appropriate and least misleading handling strategy, rather than immediately applying an imputation method.
Read the full bite: How would you handle 10% nulls in a key column?
Question 16 of 30
A product manager wants to understand if a major UI redesign caused a sustained change in user engagement over the subsequent six months. Which research method is most appropriate?
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Answer: b · A longitudinal study tracking the engagement metrics of a specific cohort of users who experienced the redesign over six months.
A longitudinal study is specifically designed to track the same users over time to observe how behavior evolves and infer causality, making it ideal for understanding the durable impact of a product change. Other options either provide only a snapshot, focus on short-term/new user impact, or offer qualitative insights without quantifying sustained behavioral change across a cohort.
Read the full bite: Longitudinal Study: Watching Change Over Time
Question 17 of 30
A researcher needs to study a population that is difficult to identify and access. Which scenario best illustrates an appropriate use of snowball sampling?
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Answer: c · Studying the communication patterns within a clandestine activist group.
Snowball sampling is ideal for populations that are hard to reach, hidden, or lack a clear sampling frame, as it leverages existing social networks to gain access. A clandestine group fits this description perfectly, unlike scenarios requiring statistical generalization or having readily available sampling frames.
Read the full bite: Snowball Sampling: When Your Users Find Your Users
Question 18 of 30
In A/B testing, when is the Minimum Detectable Effect (MDE) primarily determined and used?
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Answer: d · Before the experiment begins, to calculate the required sample size for detecting a meaningful change.
The card explicitly states that MDE is an input for experiment design, determined 'before a test' to calculate the required sample size. It is a planning tool, not an analysis tool used after the experiment or during runtime.
Read the full bite: Minimum Detectable Effect: How Small a Change Can You See?
Question 19 of 30
When setting SLOs for API latency, why can the mean alone give a misleading view of user experience?
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Answer: a · A few extreme tail values can pull the mean up and hide suffering at the p95
Latency data is right-skewed, so a handful of multi-second outliers can inflate the mean and mask terrible tail experiences. Distractor B is tempting but wrong because standard deviation assumes a normal distribution, whereas latency distributions have a long tail and a hard floor near zero.
Read the full bite: Why prefer median and p95 over mean for API latency?
Question 20 of 30
An API's latency dashboard shows a mean of 500ms but a median of 150ms. What does this discrepancy most likely indicate?
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Answer: c · Most requests complete around 150ms, but a few very slow requests are skewing the mean upward.
The median represents the typical experience. A mean that is much higher than the median indicates a right-skewed distribution with a 'long tail' of a few very slow requests, which pull the average up without affecting the midpoint.
Read the full bite: Why use median/p95 for API latency instead of the mean?
Question 21 of 30
What is the fundamental role of the null hypothesis in scientific testing?
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Answer: a · To provide a default position of no effect or no difference that requires strong evidence to overturn.
The null hypothesis establishes a baseline assumption that there is no effect or difference, acting as a default that must be disproven with sufficient evidence. Option D describes the alternative hypothesis, which represents the effect the researcher aims to demonstrate.
Read the full bite: Null Hypothesis: Assume No Effect Until Proven Otherwise
Question 22 of 30
When analyzing API response times, why are percentiles (e.g., p50, p95) generally considered more informative than the arithmetic mean?
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Answer: c · Percentiles better represent the typical and worst-case user experiences because the mean can be heavily skewed by a small number of very slow requests.
The card emphasizes that API response times often have a long-tail distribution where a few slow requests can dramatically skew the mean, making it a poor representation of most users' experiences. Percentiles like p50 (median) accurately reflect the typical user's experience, while p95/p99 capture the worst-case for the majority, directly linking to user satisfaction. Option B, while true that mean is better for normal distributions, doesn't fully capture the user-centric reason for preferring percentiles for latency, which is the core of the card's argument.
Read the full bite: Why use p50/p95 over mean for API response times?
Question 23 of 30
Without proper randomization, what is the main challenge in interpreting the results of an experiment?
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Answer: b · Determining if the observed outcomes were truly caused by the intervention being tested.
Randomization's primary purpose is to ensure that experimental groups are comparable, allowing researchers to confidently attribute observed outcome differences to the intervention. Without it, pre-existing differences between groups (confounding variables) could be mistaken for the effect of the intervention, making causal claims unreliable. Option A, while important for statistical power, addresses the quantity of data, not the quality of causal inference.
Read the full bite: Randomization: The Key to Trustworthy Experiments
Question 24 of 30
The optimizer chose a nested loop because it estimated 10 outer rows, but 5 million were returned. What is the most appropriate first action?
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Answer: c · Refresh table statistics so cardinality estimates reflect reality
The root cause is a cardinality misestimate, usually from stale statistics, so refreshing them lets the optimizer choose correctly on its own. Hints mask the problem, dropping indexes worsens it, and isolation level is unrelated to join choice.
Read the full bite: Optimizer picks nested loop over hash join
Question 25 of 30
Which scenario is most appropriate for applying a Student's t-test?
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Answer: d · Determining if a new ad campaign significantly increased sales compared to the old campaign.
The t-test is specifically used to compare the means of two groups to determine if an observed difference is statistically significant, as described in option D. Option A is incorrect because the t-test is not suitable for comparing more than two groups.
Read the full bite: Student's t-test: Is This Difference Real or Just Noise?
Question 26 of 30
Which scenario is most appropriate for applying a Chi-Squared test?
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Answer: b · Determining if there's a statistically significant association between two categorical variables.
The Chi-Squared test is specifically designed to assess the association or independence between two categorical variables, as stated in the card. It explicitly notes that the test 'only shows association, not causation,' making option D incorrect.
Read the full bite: Chi-Squared Test: Are These Two Things Related?
Question 27 of 30
A sales team member achieves a record-breaking quarter. Based on the principle of regression to the mean, what is most likely to happen in the following quarter?
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Answer: a · Their sales performance will likely decrease, moving closer to their historical average.
Regression to the mean posits that extreme outcomes, which are partly due to random chance, are unlikely to be repeated. Therefore, a record-breaking performance is most likely to be followed by a performance closer to the individual's average. Options B and C incorrectly assume the extreme performance establishes a new baseline or trend, while D overstates the expected regression.
Read the full bite: Regression to the Mean: Why Outliers Settle Down
Question 28 of 30
What is a primary drawback of applying the Bonferroni correction, especially with many comparisons?
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Answer: a · It becomes excessively conservative, making it harder to detect real effects.
The correct answer is C because the card states that with many comparisons, the Bonferroni correction 'becomes so conservative that it dramatically increases your chance of a false negative (missing a real effect).' Option C is incorrect because the Bonferroni correction's purpose is to reduce the chance of a Type I error (incorrectly rejecting a true null hypothesis), not increase it.
Read the full bite: Bonferroni Correction: Raising the Bar for Significance
Question 29 of 30
At 5% alpha, 80% power, and a 10% true-effect base rate, what should a team infer from roughly two significant wins per quarter?
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Answer: c · Approximately one of the two significant results is likely a false positive due to the low base rate
With a 10% base rate and standard 80% power and 5% alpha, roughly one-third of significant results are expected to be false positives, meaning about one of two quarterly wins is likely spurious. Distractor A repeats the common error of seeking larger samples without addressing the underlying base rate of true effects.
Read the full bite: WAU is flat despite positive A/B tests; why and how to diagnose
Question 30 of 30
Why is mean imputation often a poor default for a heavily skewed numerical column?
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Answer: a · It is pulled by outliers and shrinks the column's variance
The mean is sensitive to outliers in skewed data and filling with one constant reduces variance and distorts correlations; the median is more robust. Mean imputation keeps all rows rather than removing them.
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