Evaluate Marketing Campaign's Click-Through Rate Effectiveness
Overview
This question evaluates proficiency in statistical inference for proportions, including formal hypothesis specification (one-sided vs two-sided), interpretation of p-values and confidence intervals, and considerations of power, effect size, and Type I/II errors.
Meta
Aug 4, 2025, 10:55 AM
Data Scientist
Onsite
Statistics & Math
0
0
Scenario
A campaign currently shows a click-through rate (CTR) of 4.2%. Leadership asks whether this is good or bad relative to expectations.
Task
State and justify a formal statistical test to evaluate whether a 4.2% CTR meets expectations.
- Hypotheses: Formally state the null and alternative hypotheses. Clarify whether you would use a two-sided ("different") or one-sided ("meets or exceeds") test and why.
- Test choice: Which statistical test would you use and why? (Assume CTR follows a Binomial model.)
- Additional data needed: List what additional inputs you need (e.g., expected/benchmark CTR, sample size, time window).
- Computation: Compute the p-value and a 95% confidence interval for the CTR and interpret both statistical and practical significance.
Notes and hints:
- Model CTR as Binomial.
- A one-proportion z-test (large n) or exact Binomial test (small n) is appropriate. Use Wilson CI for proportions.
- Discuss power, effect size, and Type I/II errors.
If the benchmark and sample size are not provided, show the symbolic solution and then illustrate with a concrete example (e.g., benchmark p0 = 4.0% and n = 100,000 impressions with 4,200 clicks).
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