Let's go through each statement to determine which correctly describes the confidence interval concept:

1. "You are 95% certain that the average level of eating habits for students at ASU is 4.22."

   • Incorrect: A confidence interval does not provide certainty about a specific value like 4.22. Instead, it estimates a range in which the true population mean lies with a certain level of confidence.

2. "You are 95% confident that the actual mean level of eating habits for US college students (the true population mean) is not less than the lower limit and not greater than the upper limit of your confidence interval."

   • Correct: This is the essence of a 95% confidence interval. It means we are 95% confident that the interval contains the true population mean.

3. "If you collected a large number of samples from the population of US college students, 95 times out of 100, the true population mean would be included within your computed interval."

   • Correct: This statement describes how confidence intervals behave in the long run. If you repeatedly took samples and computed intervals, 95% of those intervals would contain the true population mean.

4. "If you collected a large number of samples from the population of US college students, 5 times out of 100 the true population mean will NOT be included in the specified interval."

   • Correct: This complements the previous statement. There is a 5% chance that any given interval will not contain the true mean.

5. "There is a 1% risk that the true population mean will not be included in the specified interval."

   • Incorrect: A 95% confidence interval implies a 5% risk, not a 1% risk. This statement would apply to a 99% confidence interval.

6. "There is a 95% risk that the true population mean will not be included in the specified interval."

   • Incorrect: A 95% confidence interval means that we are confident the true mean is within the interval 95% of the time, not that there is a 95% risk it is not. This statement is the opposite of what confidence intervals represent.

Correct Statements:

• 2, 3, and 4.

Do you want further details on how confidence intervals are computed or interpreted?

Related Questions:

1. How does the width of a confidence interval relate to sample size?
2. What happens to the confidence interval if the confidence level is increased from 95% to 99%?
3. How does the variability (standard deviation) of the data affect the confidence interval?
4. What is the difference between confidence intervals and prediction intervals?
5. How does the choice of confidence level (e.g., 90%, 95%, 99%) impact the risk of Type I error?

Tip: A smaller sample size or higher variability in the data will result in a wider confidence interval.