How can I use the calculated SEM in Excel to construct a confidence interval around an individual's observed test score?

Once you have calculated the SEM in Excel, you can use it to construct a confidence interval around an individual's observed score. This interval provides a range within which the individual's 'true score' is estimated to lie with a certain level of confidence (e.g., 68%, 95%, 99%). The general formula for a confidence interval is: **Observed Score ± (Z-score * SEM)**. Here's how to do it in Excel: 1. **Input Observed Score**: Enter the individual's observed test score into a cell (e.g., D1). 2. **Input Z-score**: Determine the appropriate Z-score for your desired confidence level: * For a 68% confidence interval, Z ≈ 1.00 * For a 95% confidence interval, Z ≈ 1.96 * For a 99% confidence interval, Z ≈ 2.58 Enter this Z-score into a cell (e.g., D2). 3. **Input SEM**: Ensure your calculated SEM is in a cell (e.g., D3). 4. **Calculate Lower Bound**: In a cell, enter the formula for the lower bound: `=D1 - (D2 * D3)`. 5. **Calculate Upper Bound**: In another cell, enter the formula for the upper bound: `=D1 + (D2 * D3)`. This will give you the range for the confidence interval. For example, if an observed score is 75, SEM is 3, and you want a 95% CI (Z=1.96): * Lower Bound: `=75 - (1.96 * 3)` = 69.12 * Upper Bound: `=75 + (1.96 * 3)` = 80.88 So, the 95% confidence interval for the true score is approximately 69.12 to 80.88.