The following data on x = the line speed (feet per minute) and y = the number of defective parts found for a production process at Brawdy Plastics provided the estimated regression equation ŷ = 27.5 – 0.3z. Excel File: data14-37.xlsx Number of Defective Line Speed Parts Found 20 23 20 21 30 19 30 16 40 15 40 17 50 14 50 11 For these data SSE = 16 Develop a 95% confidence interval for the mean number of defective parts for a line speed of 25 feet per minute (to 4 decimals). Use Table 1 of Appendix B. to

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**Educational Website Content:**

The dataset below outlines the relationship between line speed (x) in feet per minute and the number of defective parts (y) found in a manufacturing process at Brawdy Plastics. The estimated regression equation derived from these data is given by:

\[
\hat{y} = 27.5 - 0.3x
\]

**Data Table:**

| Line Speed (feet per minute) | Number of Defective Parts Found |
|-----------------------------|---------------------------------|
| 20                          | 23                              |
| 20                          | 21                              |
| 30                          | 19                              |
| 30                          | 16                              |
| 40                          | 15                              |
| 40                          | 17                              |
| 50                          | 14                              |
| 50                          | 11                              |

**Task:**

For this dataset, with an SSE (Sum of Squared Errors) of 16, we aim to develop a 95% confidence interval for the mean number of defective parts at a line speed of 25 feet per minute, calculating to four decimal places. Refer to Table 1 of Appendix B for necessary statistical values.

**Instructions:**

Calculate and enter the confidence interval using the spaces provided:
\[ \_\_\_\_\_\_\_ \text{ to } \_\_\_\_\_\_\_ \]
Transcribed Image Text:**Educational Website Content:** The dataset below outlines the relationship between line speed (x) in feet per minute and the number of defective parts (y) found in a manufacturing process at Brawdy Plastics. The estimated regression equation derived from these data is given by: \[ \hat{y} = 27.5 - 0.3x \] **Data Table:** | Line Speed (feet per minute) | Number of Defective Parts Found | |-----------------------------|---------------------------------| | 20 | 23 | | 20 | 21 | | 30 | 19 | | 30 | 16 | | 40 | 15 | | 40 | 17 | | 50 | 14 | | 50 | 11 | **Task:** For this dataset, with an SSE (Sum of Squared Errors) of 16, we aim to develop a 95% confidence interval for the mean number of defective parts at a line speed of 25 feet per minute, calculating to four decimal places. Refer to Table 1 of Appendix B for necessary statistical values. **Instructions:** Calculate and enter the confidence interval using the spaces provided: \[ \_\_\_\_\_\_\_ \text{ to } \_\_\_\_\_\_\_ \]
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