Test Statistic Calculation for Drug Effect on Blood Pressure

A researcher is testing a new drug and wants to determine if it has a significant effect on blood pressure. The null hypothesis ($H_0$) states that the drug has no effect, while the alternative hypothesis ($H_1$) posits that the drug does affect blood pressure. The researcher collects a sample of 30 patients and calculates the sample mean decrease in blood pressure to be 5 mmHg with a sample standard deviation of 2 mmHg. Given a significance level ($eta$) of 0.05, the test statistic can be calculated using the formula:

$$ t = rac{ar{x} - ext{µ}}{s / ext{√n}} $$

Where:

• $ar{x}$ = Sample mean
• µ = Population mean under the null hypothesis (assumed to be 0 for no effect)
• s = Sample standard deviation
• n = Sample size

The calculated test statistic is then compared to the critical t-value from the t-distribution with $n - 1$ degrees of freedom. What is the test statistic in this situation?