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Sample Size Planning for Signup Test

Medium
Statistics & Probability
Power AnalysisSample SizeExperimentation

Problem

Business Context

StreamCart wants to test a new signup page that may improve visitor-to-account conversion. Before launching the experiment, the product team wants to know how many users are needed to reliably detect a meaningful lift.

Problem Statement

Plan the sample size for a two-arm A/B test on conversion rate. The current signup conversion rate is 18.0%, and the team only wants to run the test if it has enough power to detect an absolute lift of at least 1.5 percentage points.

Given Data

MetricValue
Baseline conversion rate18.0%
Minimum detectable effect (absolute)1.5 percentage points
Expected treatment conversion rate19.5%
Significance level0.05
Desired power80%
Test typeTwo-sided
Traffic split50/50
Weekly eligible visitors120,000

Requirements

  1. State the null and alternative hypotheses.
  2. Compute the required sample size per group for a two-proportion test using the normal approximation.
  3. Compute the total sample size and estimated test duration in weeks.
  4. If the team can only collect 8,000 users per group, estimate the approximate power for detecting the same 1.5 percentage point lift.
  5. Explain how sample size, effect size, significance level, and power trade off in experiment planning.

Assumptions

  • Users are independently and randomly assigned.
  • The baseline rate of 18.0% is stable during the test window.
  • The normal approximation is appropriate because expected successes and failures are large in both groups.
  • Ignore multiple testing and sequential peeking for this calculation.

Sample Data

Example 1
Input{"mde_absolute":0.015,"desired_power":0.8,"significance_level":0.05,"traffic_split_control":0.5,"traffic_split_treatment":0.5,"baseline_conversion_rate":0.18,"weekly_eligible_visitors":120000,"feasible_sample_per_group":8000,"treatment_conversion_rate":0.195}Output(none)

Problem

Business Context

StreamCart wants to test a new signup page that may improve visitor-to-account conversion. Before launching the experiment, the product team wants to know how many users are needed to reliably detect a meaningful lift.

Problem Statement

Plan the sample size for a two-arm A/B test on conversion rate. The current signup conversion rate is 18.0%, and the team only wants to run the test if it has enough power to detect an absolute lift of at least 1.5 percentage points.

Given Data

MetricValue
Baseline conversion rate18.0%
Minimum detectable effect (absolute)1.5 percentage points
Expected treatment conversion rate19.5%
Significance level0.05
Desired power80%
Test typeTwo-sided
Traffic split50/50
Weekly eligible visitors120,000

Requirements

  1. State the null and alternative hypotheses.
  2. Compute the required sample size per group for a two-proportion test using the normal approximation.
  3. Compute the total sample size and estimated test duration in weeks.
  4. If the team can only collect 8,000 users per group, estimate the approximate power for detecting the same 1.5 percentage point lift.
  5. Explain how sample size, effect size, significance level, and power trade off in experiment planning.

Assumptions

  • Users are independently and randomly assigned.
  • The baseline rate of 18.0% is stable during the test window.
  • The normal approximation is appropriate because expected successes and failures are large in both groups.
  • Ignore multiple testing and sequential peeking for this calculation.

Sample Data

Example 1
Input{"mde_absolute":0.015,"desired_power":0.8,"significance_level":0.05,"traffic_split_control":0.5,"traffic_split_treatment":0.5,"baseline_conversion_rate":0.18,"weekly_eligible_visitors":120000,"feasible_sample_per_group":8000,"treatment_conversion_rate":0.195}Output(none)
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