Evaluate Marketing Campaign's Click-Through Rate Effectiveness

Q: Evaluate Marketing Campaign's Click-Through Rate Effectiveness

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.

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Question

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).

Evaluate Marketing Campaign's Click-Through Rate Effectiveness

Scenario

Task

Solution

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