A pharmaceutical company claims that a new drug reduces bloo…

A pharmaceutical company claims that a new drug reduces blood pressure more effectively than the standard drug. A clinical trial is conducted, and a hypothesis test is set up as follows:·        Null Hypothesis (H₀): The new drug is no more effective than the standard drug (mean reduction ≤ 0).·        Alternative Hypothesis (H₁): The new drug is more effective than the standard drug (mean reduction > 0).The test is conducted at a significant level, α=0.05Questions: a) Define Type I and Type II errors in the context of this study. (3)b) Suppose the actual mean improvement is 5 mmHg (i.e., the drug is more effective). Explain what a Type II error would mean in this context. (2)

You fit two linear models to predict monthly sales revenue:M…

You fit two linear models to predict monthly sales revenue:Model A uses 3 predictors and achieves R² = 0.91, Adjusted R² = 0.88.Model B uses 6 predictors and achieves R² = 0.93, Adjusted R² = 0.86.Questions: a) Explain why Model B has a higher R² but a lower Adjusted R². (2)b) Which model would you prefer and why? (1)c) How does Adjusted R² penalize complexity? (2)