Suppose a $95\%$ confidence interval for the mean difference in blood pressure between a treatment group and a control group is $(-2,5)$. Based on this interval, what does the confidence interval suggest about the effectiveness of the treatment?

• A. The confidence interval proves that the treatment is effective for all patients.
• B. The interval is entirely below $0$, so the treatment significantly decreases blood pressure.
• C. The interval includes $0$, so there is not enough evidence to conclude that the treatment has a significant effect on blood pressure.
• D. The interval is entirely above $0$, so the treatment significantly increases blood pressure.

Answer: (C)

Verified step by step guidance

1. Understand that a 95% confidence interval for the mean difference in blood pressure is given as (-2, 5). This interval estimates the range in which the true mean difference lies with 95% confidence.
2. Recall that if the confidence interval includes zero, it means that zero is a plausible value for the mean difference, indicating no significant difference between the treatment and control groups.
3. Check the interval endpoints: since the interval ranges from -2 to 5, zero lies within this interval.
4. Interpret this inclusion of zero as evidence that we cannot reject the null hypothesis of no difference; therefore, there is not enough statistical evidence to conclude that the treatment has a significant effect on blood pressure.
5. Conclude that the confidence interval suggests the treatment effect is not statistically significant, meaning the treatment may not have a consistent impact on blood pressure across patients.