As a domain expert in statistics, I can tell you that confidence intervals are an essential tool in inferential statistics. They provide a range of values that are likely to contain an unknown population parameter. Here's why we need them and how they work:


1. Estimation of Population Parameters: Confidence intervals are used to estimate population parameters when it is not feasible to measure the entire population. They give us a range, not a single point estimate, which reflects the uncertainty inherent in the estimation process.


2. Quantifying Uncertainty: Unlike a point estimate, a confidence interval quantifies the uncertainty associated with the estimate. It tells us how precise our estimate is. This is particularly important in scientific research, where it's crucial to understand the level of confidence in the results.


3. Statistical Decision Making: In many cases, decisions are made based on statistical data. A confidence interval provides a range within which the true value is likely to fall, which is more informative for decision-making than a single point estimate.


4. Replicability and Repeatability: Confidence intervals help in assessing the replicability of results. If different studies produce confidence intervals that overlap, it suggests that the results are consistent and repeatable.


5. Comparison of Groups: They are also used to compare two or more groups. If the confidence intervals of two groups do not overlap, it suggests a significant difference between the groups.

6. **Avoiding Over-Reliance on a Single Number**: Relying solely on a point estimate can be misleading because it doesn't convey the variability or the range of possible values. A confidence interval provides a more complete picture.

7.
Hypothesis Testing: In hypothesis testing, confidence intervals are used to determine whether there is a statistically significant difference between the sample and the population.

8.
Practical Significance: Confidence intervals also help in determining the practical significance of the results, not just the statistical significance.

9.
Transparency in Reporting: Reporting confidence intervals is a more transparent way of reporting results. It allows other researchers to assess the reliability of the findings.

10.
Planning Future Studies: The width of the confidence interval can guide the planning of future studies. A wide interval might indicate the need for a larger sample size to achieve a more precise estimate.

Now, let's move on to the translation:

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A confidence interval is a range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter. Because of their random nature, it is unlikely that two samples from a given population will yield identical confidence intervals.Apr 18, 2013read more >>