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It looks like you're working on a problem involving **confidence intervals** and missing values for the margin of error (ME) or sample means.

In the table, you are given the sample mean (\( \bar{x} \)), margin of error (ME), lower limit, and upper limit of three intervals. Based on the confidence interval formula:

\[
\text{Lower Limit} = \bar{x} - \text{ME}
\]
\[
\text{Upper Limit} = \bar{x} + \text{ME}
\]

Let's analyze the missing data and solve for it.

### Interval 1:
- **Given**: Sample Mean = 130.4, Lower Limit = 121.90, Upper Limit = 141.82
- **Missing**: Margin of Error

To find the margin of error (ME):

\[
\text{ME} = \text{Upper Limit} - \bar{x} = 141.82 - 130.4 = 11.42
\]

So, the correct margin of error for Interval 1 is **11.42**.

---

### Interval 2:
- **Given**: Sample Mean = 136.57, ME = 8.55, Upper Limit = 145.12
- **Missing**: Lower Limit

Using the formula for the lower limit:

\[
\text{Lower Limit} = \bar{x} - \text{ME} = 136.57 - 8.55 = 128.02
\]

The lower limit is already correct in this case.

---

### Interval 3:
- **Given**: Sample Mean = 165.31, ME = 17.37, Lower Limit = 147.94, Upper Limit = 182.68
- No values are missing for this interval, everything is complete and correct.

---

### Final Table:

| Interval  | Sample Mean | Margin of Error | Lower Limit | Upper Limit |
|-----------|--------------|-----------------|-------------|-------------|
| Interval 1| 130.4        | **11.42**        | 121.90      | 141.82      |
| Interval 2| 136.57       | 8.55             | 128.02      | 145.12      |
| Interval 3| 165.31       | 17.37            | 147.94      | 182.68      |

---

Would you like a deeper explanation of confidence intervals or how the margin of error is calculated?

### Follow-up questions:
1. What is a confidence interval and how is it interpreted?
2. How does sample size affect the width of a confidence interval?
3. What assumptions must be met for a confidence interval to be valid?
4. How is the margin of error related to the standard deviation of the sample?
5. Can confidence intervals be used for proportions as well as means?

**Tip:** The width of a confidence interval (upper limit - lower limit) is directly affected by the margin of error, which in turn depends on the sample size and variability of the data.

Use your knowledge of the confidence interval to determine the missing values for the 3 confidence intervals in the table below. Report answers accurate to 2 (two) decimal places.

Learn how to solve confidence interval problems by finding missing values such as the margin of error, lower limit, and upper limit. This example involves statistical concepts, including sample mean and margin of error. Suitable for Grades 9-12.

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