Business Context
NovaBio is testing whether a new treatment improves patient recovery rates versus the current standard of care. A research analyst needs to formalize the hypothesis test and determine whether the observed improvement is statistically credible.
Problem Statement
You are given results from a randomized study comparing recovery within 30 days for patients on the standard treatment and patients on a new treatment. Use a hypothesis test for two proportions to evaluate whether the new treatment changes recovery rates.
Given Data
| Group | Sample Size | Recovered Within 30 Days | Recovery Rate |
|---|
| Standard treatment | 320 | 182 | 56.9% |
| New treatment | 300 | 195 | 65.0% |
Additional parameters:
| Parameter | Value |
|---|
| Significance level | 0.05 |
| Test type | Two-tailed |
Requirements
- State the null and alternative hypotheses.
- Compute the sample recovery rates for both groups.
- Calculate the pooled proportion under the null hypothesis.
- Compute the standard error and z-statistic for a two-proportion z-test.
- Find the two-tailed p-value and make a decision at α=0.05.
- Construct a 95% confidence interval for the difference in recovery rates.
- Explain how you would communicate the result to a research lead deciding whether to fund a larger trial.
Assumptions
- Patients were randomly assigned to treatment groups.
- Outcomes are independent across patients.
- Sample sizes are large enough for the normal approximation to be reasonable.
- No major protocol deviations or differential dropout affected one group more than the other.
