Business Context
NovaBio is testing whether a new migraine treatment improves the average reduction in monthly migraine days compared with the current standard treatment. A research analyst needs to evaluate whether the observed improvement is statistically meaningful.
Problem Statement
Use a two-sample hypothesis test for means to determine whether the new treatment leads to a larger average reduction in monthly migraine days than the standard treatment.
Given Data
| Group | Sample Size | Mean Reduction in Migraine Days | Sample Standard Deviation |
|---|
| Standard treatment | 64 | 3.8 days | 1.9 days |
| New treatment | 70 | 4.4 days | 2.1 days |
Additional test settings:
| Parameter | Value |
|---|
| Significance level | 0.05 |
| Test type | One-tailed |
Requirements
- State the null and alternative hypotheses.
- Compute the standard error for the difference in sample means.
- Calculate the test statistic.
- Estimate the p-value using the normal approximation.
- Decide whether to reject the null hypothesis at α=0.05.
- Construct a 95% confidence interval for the difference in means.
- Interpret the result in research and business terms.
Assumptions
- The two patient groups were independently randomized.
- Sample sizes are large enough for the sampling distribution of the mean difference to be approximately normal.
- Monthly migraine-day reduction is measured consistently across both groups.
- Use the large-sample two-sample z-test approximation for this exercise.
