1. What is Confidence Interval?

A Confidence Interval (CI) is a range of values that is likely to contain a population parameter with a certain level of confidence. It provides an estimated range of values which is likely to include an unknown population parameter.

2. How Does the Calculator Work?

The calculator uses the Confidence Interval formula:

Where:

• \( Statistic \) — The sample statistic (mean, proportion, etc.)
• \( Critical\ Value \) — The value from statistical distribution (z-score or t-score)
• \( SE \) — Standard Error of the statistic

Explanation: The confidence interval provides a range around the sample statistic that likely contains the true population parameter.

3. Importance of Confidence Interval

Details: Confidence intervals are crucial in statistical inference as they provide a range of plausible values for population parameters and indicate the precision of estimate.

4. Using the Calculator

Tips: Enter the sample statistic, appropriate critical value (z-score or t-score), and standard error. All values must be valid numeric values.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between 90%, 95%, and 99% confidence levels?
A: Higher confidence levels produce wider intervals. 95% confidence means if we repeated the study many times, 95% of the intervals would contain the true parameter.

Q2: How do I choose the correct critical value?
A: Critical values depend on the confidence level and sample size. For large samples use z-scores, for small samples use t-scores with appropriate degrees of freedom.

Q3: What does a narrower confidence interval indicate?
A: A narrower interval indicates more precise estimate of the population parameter, typically resulting from larger sample sizes or lower variability.

Q4: Can confidence intervals be used for hypothesis testing?
A: Yes, if the null hypothesis value falls outside the confidence interval, you can reject the null hypothesis at the corresponding significance level.

Q5: What are common misinterpretations of confidence intervals?
A: Common errors include thinking the interval contains the parameter with certain probability (it's fixed) or that 95% of sample statistics fall within the interval.