Final answer:
The standard error of the mean difference in blood pressure is 1.2 mmHg. The 95% Confidence Interval is between 2.946 and 7.654 mmHg, suggesting a reduction in blood pressure. This interval indicates effectiveness of the drug with 95% confidence.
Step-by-step explanation:
To assess the effectiveness of the drug using the mean decrease in blood pressure, we can calculate the standard error of the mean difference (Δ) using the sample mean of the differences (d-) and the sample variance. The standard error (SE) is given by the formula:
SE = √(variance / sample size)
In this case, the sample variance is 144.0 and the sample size is 100. So, the standard error is:
SE = √(144.0 / 100) = √1.44 = 1.2
To construct a 95% confidence interval (CI) for the population mean of d, we use the formula:
CI = sample mean ± (z-score * standard error)
The z-score for a 95% CI is typically 1.96. Therefore, the 95% CI is:
CI = 5.3 ± (1.96 * 1.2) = (2.946, 7.654)
The 95% CI suggests that we can be 95% confident that the true mean decrease in blood pressure lies between 2.946 and 7.654 millimeters of mercury after taking the drug. A positive mean decrease indicates that on average, the blood pressure has reduced after consuming the drug. This provides evidence towards the effectiveness of the drug.
In terms of the interpretation, a 95% confidence interval means that if the experiment were repeated many times, 95% of the calculated confidence intervals would capture the true population mean.