Business Context

MetroPulse Analytics is supporting a high-profile city transit initiative. Before publishing a public-facing report, the team wants to verify that support estimates are not biased by an unrepresentative sample.

Problem Statement

A citywide survey measured resident support for the initiative, but the sample over-represented high-income residents. You are asked to test whether the observed support rate in the raw sample differs significantly from the support rate after demographic reweighting. This is a simple statistical check to assess whether sampling bias may materially affect the conclusion.

Given Data

Treat the reweighted estimate as an independent benchmark for this exercise.

Requirements

1. State the null and alternative hypotheses for whether the raw and reweighted support rates differ.
2. Compute the pooled proportion.
3. Calculate the standard error for the difference in proportions.
4. Compute the z-statistic and two-tailed p-value.
5. Construct a 95% confidence interval for the difference in support rates.
6. Conclude whether the raw analysis appears materially biased and explain what this implies for reporting the initiative's support level.

Assumptions

• Responses are independent within each estimate.
• The normal approximation is appropriate for proportions at these sample sizes.
• The reweighted estimate is treated as a valid adjustment benchmark.
• No additional multiple-testing correction is required because this is a single pre-publication bias check.