Find 99% Confidence Interval Calculator

99% Confidence Interval Formula:

\[ \text{lower} = \text{mean} - 2.576 \times \left(\frac{s}{\sqrt{n}}\right) \] \[ \text{upper} = \text{mean} + 2.576 \times \left(\frac{s}{\sqrt{n}}\right) \]

Lower Bound:

Upper Bound:

Mean:

Standard Deviation:

Sample Size:

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1. What is a 99% Confidence Interval?

A 99% confidence interval is a range of values that is likely to contain the population parameter with 99% confidence. It means if we were to take many samples and build a confidence interval from each, we would expect about 99% of them to contain the true population mean.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ \text{lower} = \text{mean} - 2.576 \times \left(\frac{s}{\sqrt{n}}\right) \] \[ \text{upper} = \text{mean} + 2.576 \times \left(\frac{s}{\sqrt{n}}\right) \]

Where:

\( \text{mean} \) — Sample mean
\( s \) — Sample standard deviation
\( n \) — Sample size
2.576 — Z-score for 99% confidence level

Explanation: The margin of error is calculated using the standard error (s/√n) multiplied by the critical z-value for 99% confidence (2.576).

3. Importance of Confidence Intervals

Details: Confidence intervals provide a range of plausible values for the population parameter and give more information than just a point estimate. A 99% CI is wider than a 95% CI but provides greater confidence that it contains the true parameter.

4. Using the Calculator

Tips: Enter the sample mean, sample standard deviation, and sample size. The calculator will compute the lower and upper bounds of the 99% confidence interval.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a 99% CI instead of 95% CI?
A: Use a 99% CI when you need greater confidence in your interval estimate, accepting that it will be wider than a 95% CI.

Q2: What assumptions does this calculator make?
A: It assumes the sampling distribution is approximately normal (or n is large enough for CLT to apply) and that the sample is representative.

Q3: Why is the z-score 2.576 for 99% CI?
A: This value comes from the standard normal distribution, representing the point where 99% of the area under the curve is contained within ±2.576 standard deviations.

Q4: Can I use this for small sample sizes?
A: For small samples (typically n < 30), consider using the t-distribution instead of the z-distribution.

Q5: How does sample size affect the CI?
A: Larger sample sizes result in narrower confidence intervals, as the standard error decreases with increasing n.