To determine the risk difference and its 95% confidence interval, you need to go through the following steps:
### Step 1: Identify the Risks and Their Confidence Intervals
The given risks and their confidence intervals are:
1. Risk 1: [tex]\(0.19\)[/tex] with CI [tex]\((0.11, 0.27)\)[/tex]
2. Risk 2: [tex]\(2.33\)[/tex] with CI [tex]\((1.7, 3.3)\)[/tex]
3. Risk 3: [tex]\(3.00\)[/tex] with CI [tex]\((1.9, 4.7)\)[/tex]
4. Risk 4: [tex]\(2.33\)[/tex] with CI [tex]\((0.09, 3.3)\)[/tex]
### Step 2: Determine the Highest and Lowest Risks
From the given risks, identify the maximum and minimum values.
- Highest risk: [tex]\(3.00\)[/tex]
- Lowest risk: [tex]\(0.19\)[/tex]
### Step 3: Calculate the Risk Difference
The risk difference is calculated as the difference between the highest risk and the lowest risk.
[tex]\[ \text{Risk Difference} = 3.00 - 0.19 = 2.81 \][/tex]
### Step 4: Determine the 95% Confidence Interval for the Risk Difference
To calculate the 95% confidence interval for the risk difference, you need to consider the lower bound of the smallest lower limit and the upper bound of the highest upper limit from the given confidence intervals.
- Minimum of lower bounds: [tex]\( \min(0.11, 1.7, 1.9, 0.09) = 0.09 \)[/tex]
- Maximum of upper bounds: [tex]\( \max(0.27, 3.3, 4.7, 3.3) = 4.7 \)[/tex]
Therefore, the 95% confidence interval for the risk difference is:
[tex]\[ \text{95% CI} = (0.09, 4.7) \][/tex]
### Final Answer
The risk difference and its 95% confidence interval are:
[tex]\[ \text{Risk Difference} = 2.81 \][/tex]
[tex]\[ \text{95% Confidence Interval} = (0.09, 4.7) \][/tex]
