Confidence Interval Interpretation for Email Test

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Business Context

BrightCart, an online retail platform, tested a new promotional email subject line to improve purchase conversion. The analytics team wants to know how to interpret the result when the confidence interval for lift includes zero.

Problem Statement

A 10-day A/B test compared the current subject line (control) against a new subject line (treatment). Your task is to evaluate whether the treatment changed conversion rate and explain what it means if the confidence interval for the treatment effect crosses zero.

Given Data

Group	Sample Size	Purchases	Conversion Rate
Control	8,200	656	8.00%
Treatment	8,050	684	8.50%

Additional test settings:

Metric	Value
Observed lift	0.50 percentage points
Significance level	0.05
Confidence level	95%

Requirements

State the null and alternative hypotheses for the conversion-rate difference.
Compute the observed difference in proportions.
Calculate the standard error for the unpooled difference in proportions.
Construct the 95% confidence interval for the treatment minus control lift.
Determine whether the interval crosses zero and what that implies statistically.
Explain the business interpretation: should BrightCart roll out the new subject line now?

Assumptions

Users were randomly assigned to control and treatment.
Each user received only one email and is counted once.
The normal approximation is appropriate because both groups have large sample sizes and enough conversions/non-conversions.
No major delivery or tracking issues affected one group differently.