# Analyze survey with gender imbalance ## Scenario You ran a user survey to measure satisfaction with a new product feature. Each respondent reports: - `gender ∈ {female, male}` - `satisfaction` (e.g., binary satisfied/not satisfied, or a 1–5 Likert score) After data collection, you notice the survey respondents are **not gender-balanced** (e.g., the female/male split in respondents differs from the true split in your user population). ## Questions 1. **What are the key concerns** with using this survey to estimate overall satisfaction for the full user population? 2. **How would you validate** whether the imbalance is problematic (i.e., whether it biases your estimate)? What checks or additional data would you use? 3. **What distributional assumptions** might you make for: - the gender counts in the sample (female vs male), and - the satisfaction outcome within each gender? Explain when those assumptions are reasonable. 4. Compute the probability of observing exactly **30 female respondents out of 70 total respondents**: - (a) if each respondent is sampled independently from a population where the true female proportion is `p`, and - (b) if you sampled *without replacement* from a finite population of size `N` with `F` females. 5. How would **stratified sampling** help here, and how would you analyze the results if you used stratified sampling (including how to combine strata to estimate overall satisfaction)? ### Clarifying Questions to Ask - Clarify the random variables, distributional assumptions, independence assumptions, and desired output. - Show enough derivation for the interviewer to follow the reasoning. - Explain how you would validate the result with simulation or sensitivity checks. ### What a Strong Answer Covers - A correct setup with definitions, formulas, and boundary conditions. - A step-by-step derivation or estimation plan. - Interpretation of the result, including uncertainty and practical limitations. - Checks for assumptions, edge cases, and numerical stability. ### Follow-up Questions - How would the result change if the assumptions were relaxed? - Can you verify the answer with a simulation? - What is the most likely source of estimation error?