The average cholesterol level for a random sample of 25 adult women from Dairyhaven, Wisconsin is 250 units (mg per dl of blood). The sample standard deviation is 35 units. Find a 95% confidence interval for the mean cholesterol level of all adult women in Dairyhaven, Wisconsin.

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### Confidence Interval Calculation for Cholesterol Levels

The average cholesterol level for a random sample of 25 adult women from Dairyhaven, Wisconsin is 250 units (mg per dl of blood). The sample standard deviation is 35 units. The task is to find a 95% confidence interval for the mean cholesterol level of all adult women in Dairyhaven, Wisconsin.

Below is a structured table to guide the calculation:

| Parameter                | Value                           |
|--------------------------|---------------------------------|
| x-bar (Sample Mean)      |                                 |
| std dev (Standard Deviation) |                                 |
| n (Sample Size)          |                                 |
| Confidence Level         |                                 |
| Margin of Error          |                                 |
| Point Estimate           |                                 |
| Lower Limit              |  **Round off to 2 decimal places**   |
| Upper Limit              |  **Round off to 2 decimal places**   |

### Explanation:

- **x-bar**: This is the sample mean, which in this case is 250 units.
- **std dev**: This is the sample standard deviation, given as 35 units.
- **n**: This is the sample size, which is 25.
- **Confidence Level**: For a 95% confidence interval, the confidence level is 95%.
- **Margin of Error**: Calculated using the formula \( Z \times \frac{\sigma}{\sqrt{n}} \), where \( Z \) is the Z-value from the standard normal distribution table that corresponds to the 95% confidence level (typically 1.96), \( \sigma \) is the standard deviation, and \( n \) is the sample size.
- **Point Estimate**: This is typically the sample mean (x-bar) in confidence interval calculations.
- **Lower Limit and Upper Limit**: Computed using the formulas (Point Estimate - Margin of Error) and (Point Estimate + Margin of Error), respectively.

### Interpretation of the Confidence Interval:
Provide a detailed explanation regarding what the confidence interval implies in the context of this problem.

By completing this table and the calculations, we'll derive a range that we can be 95% confident contains the true mean cholesterol level for all adult women in Dairyhaven, Wisconsin.
Transcribed Image Text:### Confidence Interval Calculation for Cholesterol Levels The average cholesterol level for a random sample of 25 adult women from Dairyhaven, Wisconsin is 250 units (mg per dl of blood). The sample standard deviation is 35 units. The task is to find a 95% confidence interval for the mean cholesterol level of all adult women in Dairyhaven, Wisconsin. Below is a structured table to guide the calculation: | Parameter | Value | |--------------------------|---------------------------------| | x-bar (Sample Mean) | | | std dev (Standard Deviation) | | | n (Sample Size) | | | Confidence Level | | | Margin of Error | | | Point Estimate | | | Lower Limit | **Round off to 2 decimal places** | | Upper Limit | **Round off to 2 decimal places** | ### Explanation: - **x-bar**: This is the sample mean, which in this case is 250 units. - **std dev**: This is the sample standard deviation, given as 35 units. - **n**: This is the sample size, which is 25. - **Confidence Level**: For a 95% confidence interval, the confidence level is 95%. - **Margin of Error**: Calculated using the formula \( Z \times \frac{\sigma}{\sqrt{n}} \), where \( Z \) is the Z-value from the standard normal distribution table that corresponds to the 95% confidence level (typically 1.96), \( \sigma \) is the standard deviation, and \( n \) is the sample size. - **Point Estimate**: This is typically the sample mean (x-bar) in confidence interval calculations. - **Lower Limit and Upper Limit**: Computed using the formulas (Point Estimate - Margin of Error) and (Point Estimate + Margin of Error), respectively. ### Interpretation of the Confidence Interval: Provide a detailed explanation regarding what the confidence interval implies in the context of this problem. By completing this table and the calculations, we'll derive a range that we can be 95% confident contains the true mean cholesterol level for all adult women in Dairyhaven, Wisconsin.
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