1. What is an Interval Estimate?

An interval estimate provides a range of values within which a population parameter is likely to fall, with a certain degree of confidence. It's more informative than a point estimate alone as it accounts for sampling variability.

2. How Does the Calculator Work?

The calculator uses the interval estimate formula:

Where:

• \( \text{mean} \) — Sample mean or point estimate
• \( z \) — Critical value from standard normal distribution
• \( \text{se} \) — Standard error of the estimate

Explanation: The interval is constructed by adding and subtracting the margin of error (z × se) from the point estimate.

3. Importance of Interval Estimates

Details: Interval estimates provide information about the precision of an estimate and the uncertainty associated with it. They are fundamental in hypothesis testing and statistical inference.

4. Using the Calculator

Tips: Enter the sample mean, appropriate z-score for your desired confidence level (e.g., 1.96 for 95% CI), and standard error. All values must be valid (SE > 0).

5. Frequently Asked Questions (FAQ)

Q1: How do I choose the right z-score?
A: Common z-scores are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI). The exact value depends on your desired confidence level.

Q2: What's the difference between standard deviation and standard error?
A: Standard deviation measures variability in data, while standard error measures the precision of the sample mean as an estimate of the population mean.

Q3: When should I use a t-score instead of z-score?
A: Use t-scores when sample sizes are small (typically n < 30) and population standard deviation is unknown.

Q4: How does sample size affect the interval?
A: Larger samples produce smaller standard errors and narrower intervals, all else being equal.

Q5: Can this be used for proportions?
A: Yes, with appropriate calculation of standard error for proportions (√[p(1-p)/n]).