Calculate expected value for click-through rates
Last updated: January 21, 2026
Quick Overview
Given the following scenario about user conversion, calculate the the p-value.
Roblox
January 21, 2026196
6
3,137 solved
Given the following scenario about user conversion, calculate the the p-value.
This statistics question from Roblox's Technical Screen tests your ability to apply mathematical reasoning to practical problems. The interviewer expects precise definitions, correct methodology, and awareness of assumptions and limitations.
What the Interviewer Expects
- State the correct formula or theorem with clear definitions
- Apply the concept to the given scenario step by step
- Interpret the result in plain language
- Identify assumptions and when they might be violated
Key Topics to Cover
How to Approach This
- Define your hypotheses (H0 and H1) clearly before performing any test.
- Calculate required sample size BEFORE running an experiment, using power analysis.
- Remember the Central Limit Theorem: sample means become approximately normal with large n.
- Watch for Simpson's paradox. Always segment data by key dimensions.
- Distinguish between statistical significance and practical significance.
Possible Follow-up Questions
- What alternative statistical method could you use here?
- How would you handle multiple comparisons?
- How would you explain this result to a non-technical audience?
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Problem formulation
To calculate the expected value for click-through rates (CTR) in the context of user conversion for Roblox, we need to define relevant variables. Let:
- = Total number of users exposed to an a...
Solution approach
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Calculate the observed click-through rate (CTR): Using the numbers given, calculate the CTR as follows:
-
**F...
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