Compute weighted response rates by job category

You are given a CSV file with one row per job posting and the following columns:

• job_id
• job_category
• invitations_sent (integer, expected to be >= 0)
• provider_responses (integer, expected to be >= 0)
• region
• created_at (ISO date)

Write pandas code that does the following:

1. Compute a per-job response_rate = provider_responses / invitations_sent. Treat invitations_sent = 0 as missing and exclude those rows.
2. Produce an invitation-weighted response rate for each job_category, with a 95% Wilson score confidence interval.
3. Return the top 5 job_category values ranked by the weighted response rate, breaking ties by the lower bound of the confidence interval.
4. Handle outliers robustly: rows where provider_responses > invitations_sent, rows with negative values, and rows with impossible dates must be logged and dropped.
5. Verify that the job-level weighted average equals the overall response rate computed from the aggregated numerators and denominators, within a tolerance of 1e-9.