Business Context
StayNest, a hotel booking platform, noticed that guest booking conversion appeared higher on weekends than weekdays. The analytics team wants to turn this observed trend into a formal, testable hypothesis before changing marketing spend.
Problem Statement
Using booking session data from the last 30 days, determine whether weekend traffic truly converts at a higher rate than weekday traffic, or whether the observed difference could be due to random variation.
Given Data
| Segment | Sessions | Completed Bookings | Conversion Rate |
|---|
| Weekday | 18,420 | 2,026 | 11.00% |
| Weekend | 7,860 | 1,001 | 12.74% |
Assume the team wants to test whether the weekend conversion rate is higher than the weekday conversion rate at a significance level of 5%.
Requirements
- Formulate the null and alternative hypotheses for this business question.
- Choose the appropriate statistical test and explain why it fits the data.
- Compute the pooled conversion rate under the null hypothesis.
- Calculate the standard error and z-statistic.
- Compute the one-sided p-value.
- State whether the result is statistically significant at α=0.05.
- Construct a 95% confidence interval for the difference in conversion rates.
- Interpret whether StayNest should immediately shift more budget to weekends.
Assumptions
- Sessions are independently observed.
- Each session is classified correctly as weekday or weekend.
- Sample sizes are large enough for a normal approximation to the binomial.
- No major campaign, outage, or pricing change affected only one segment during the measurement window.
