Test Billboard Campaign Conversion Rate Exceeds 60%

Q: Test Billboard Campaign Conversion Rate Exceeds 60%

This question evaluates a candidate's competency in hypothesis testing for proportions, specifically computing the standard error, a 95% confidence interval, and interpreting whether an observed conversion rate statistically exceeds a benchmark.

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Question

One-Proportion Test for a Conversion Rate

Context

You ran a billboard campaign and measured conversions on a sample of N = 100 users. The observed conversion rate is 65% (p̂ = 0.65). You want to test whether the true conversion rate exceeds 60%.

Task

State the null and alternative hypotheses for a one-sided test.
Compute the standard error (SE), 95% margin of error, and the 95% confidence interval (CI) for the conversion rate.
Using the CI, decide whether to reject H0 at α = 0.05 and interpret the result.

Hint: Use SE = sqrt(p̂(1−p̂)/N); margin = 1.96 × SE; compare the CI’s lower bound with 0.60.

Test Billboard Campaign Conversion Rate Exceeds 60%

One-Proportion Test for a Conversion Rate

Context

Task

Solution

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