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Determine Normality of Single Observation with Z-Test | Google Interview Question

Determine Normality of Single Observation with Z-Test

Last updated: Mar 29, 2026

Quick Overview

This question evaluates understanding of hypothesis testing fundamentals, specifically the ability to formulate null and alternative hypotheses and specify a decision rule for a single observation against a fully specified reference distribution.

Google

Jul 12, 2025, 6:59 PM

Data Scientist

Technical Screen

Statistics & Math

Hypothesis Test for a Single Observation Against a Standard Normal

Context

You observe a single numeric value, x, and want to decide whether it could plausibly have been drawn from a standard normal distribution N(0, 1). Assume the reference distribution (mean = 0, variance = 1) is fully specified and not estimated from data.

Question

Which statistical test would you use?
State the null and alternative hypotheses.
Give the decision rule at a chosen significance level α.

Solution

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