Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
A confidence interval is an estimated range of values which is likely to include the population parameter.
Here's a detailed explanation for this definition:
1. What is a Confidence Interval?
- A confidence interval represents a range of values, derived from sample statistics, that is likely to contain the true value of an unknown population parameter.
2. Purpose of a Confidence Interval:
- The main purpose of a confidence interval is to provide an estimate for a population parameter (such as a population mean or proportion) along with an indication of uncertainty or variability in that estimate.
3. Interpretation:
- For example, if you have a 95% confidence interval for a population mean, it means that you are 95% confident that the true population mean falls within this interval. In essence, if you were to take many samples and build confidence intervals in the same way, approximately 95% of those intervals would contain the true population parameter.
4. Components of a Confidence Interval:
- A confidence interval typically consists of:
- A point estimate (e.g., sample mean).
- A margin of error which accounts for sampling variability.
- The confidence level which reflects how certain we are that the interval contains the population parameter.
5. Answering the Options:
- An estimated range of values likely to include the population parameter: This is the correct definition of a confidence interval.
- A single value used to estimate a population parameter: This describes a point estimate, not a confidence interval.
- The difference between the highest and lowest values in a sample: This describes the range of the sample data, not related to a confidence interval.
- The range within one standard deviation of the mean: This describes a specific range around the mean, often related to the empirical rule in normal distributions, but it does not account for the concept of a confidence interval.
In conclusion, a confidence interval is best defined as an estimated range of values which is likely to include the population parameter. This provides a more comprehensive understanding of the uncertainty inherent in the sample estimate and the likely range within which the true population parameter lies.
Here's a detailed explanation for this definition:
1. What is a Confidence Interval?
- A confidence interval represents a range of values, derived from sample statistics, that is likely to contain the true value of an unknown population parameter.
2. Purpose of a Confidence Interval:
- The main purpose of a confidence interval is to provide an estimate for a population parameter (such as a population mean or proportion) along with an indication of uncertainty or variability in that estimate.
3. Interpretation:
- For example, if you have a 95% confidence interval for a population mean, it means that you are 95% confident that the true population mean falls within this interval. In essence, if you were to take many samples and build confidence intervals in the same way, approximately 95% of those intervals would contain the true population parameter.
4. Components of a Confidence Interval:
- A confidence interval typically consists of:
- A point estimate (e.g., sample mean).
- A margin of error which accounts for sampling variability.
- The confidence level which reflects how certain we are that the interval contains the population parameter.
5. Answering the Options:
- An estimated range of values likely to include the population parameter: This is the correct definition of a confidence interval.
- A single value used to estimate a population parameter: This describes a point estimate, not a confidence interval.
- The difference between the highest and lowest values in a sample: This describes the range of the sample data, not related to a confidence interval.
- The range within one standard deviation of the mean: This describes a specific range around the mean, often related to the empirical rule in normal distributions, but it does not account for the concept of a confidence interval.
In conclusion, a confidence interval is best defined as an estimated range of values which is likely to include the population parameter. This provides a more comprehensive understanding of the uncertainty inherent in the sample estimate and the likely range within which the true population parameter lies.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
