Business Context

NovaBio is reviewing results from a small clinical research study on a new blood-pressure drug. The research lead wants a quick statistical assessment of treatment effect and the relationship between dosage and blood pressure reduction.

Problem Statement

You are given summary results from a randomized study with treatment and control groups, plus a simple linear relationship between dosage and systolic blood pressure reduction among treated patients. Determine whether the drug shows a statistically significant mean improvement over control and quantify the dosage-response relationship.

Given Data

Additional regression output from treated patients only:

Use a two-sided significance level of 0.05.

Requirements

1. State the null and alternative hypotheses for the difference in mean BP reduction.
2. Compute the standard error for the difference in means.
3. Calculate the test statistic and approximate p-value for a two-sample test.
4. Construct a 95% confidence interval for the treatment effect.
5. Using the correlation result, compute the simple linear regression slope of BP reduction on dosage.
6. Interpret both the hypothesis test and the regression result in research terms.

Assumptions

• Patients were randomly assigned to treatment and control.
• Outcomes are independent across patients.
• The sample sizes are large enough for a normal approximation for the difference in means.
• The dosage-response relationship is approximately linear within the observed range.