The 95% confidence interval for these parts is 56.98 to 57.05 under normal operations. A systematic sample is taken from the manufacturing line to determine if the production process is still within acceptable levels. The mean of the sample is 56.99. What should be done about the production line?

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5DE. Given a confidence interval and sample mean, what decisions can be made (Links to an external site.)Open this document with ReadSpeaker docReader Links to an external site.(DOCX)

Group of answer choices

Stop the line as it is outside the confidence interval

Stop the line as it is inside the confidence interval

Keep the line operating as it is inside the confidence interval

Keep the line operating as it is outside the confidence interval

To determine the appropriate action for the production line, let's review the given information and the nature of confidence intervals.

1. The 95% confidence interval for the parts is from 56.98 to 57.05.
2. A sample mean of 56.99 was obtained.

A confidence interval provides a range of values within which we expect the true population mean to fall, with a specified level of confidence (in this case, 95%). If the sample mean falls within this interval, it suggests that the production process is likely operating correctly and within acceptable levels.

Given the provided confidence interval (56.98 to 57.05) and the sample mean (56.99):

- The sample mean of 56.99 falls within the confidence interval of 56.98 to 57.05.

### Decision:
Since the sample mean is within the confidence interval, it indicates that the production process is likely still operating within acceptable levels. Therefore, the appropriate action would be:

**Keep the line operating as it is inside the confidence interval.**

### Group of answer choices:
- Keep the line operating as it is inside the confidence interval.

Would you like more details or have any questions about this conclusion?

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Here are some additional questions that expand on the information provided:

1. What is the purpose of using a confidence interval in quality control?
2. How does the sample size affect the width of a confidence interval?
3. What factors could lead to a sample mean falling outside the confidence interval?
4. How can you calculate a confidence interval for a given dataset?
5. What is the impact of increasing the confidence level from 95% to 99% on the confidence interval?
6. How would you handle a situation where the sample mean is very close to the boundary of the confidence interval?
7. What other statistical measures can be used alongside confidence intervals to assess production quality?
8. How can systematic sampling be effectively implemented in a manufacturing process?

**Tip:** When interpreting confidence intervals, always consider the sample size and the potential for sampling error, as these factors can influence the reliability of your conclusions.

Learn how to determine production line status using confidence intervals. Explore an example where a sample mean falls within a 95% confidence interval (56.98 to 57.05), indicating the production process is operating within acceptable levels.

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