Confidence Interval Calculator: Free Statistics Tool
Confidence Interval Calculator
Calculate the confidence interval range for a population mean given sample data.
CONFIDENCE INTERVAL RANGE
Interval: [0.00, 0.00]
Margin of Error: 0.00
What is a Confidence Interval?
In inferential statistics, a **Confidence Interval** provides a range of values derived from sample statistics that is likely to contain the value of an unknown population parameter. For instance, a 95% confidence level implies that if you were to repeat an experiment numerous times, roughly 95% of the calculated intervals would successfully contain the true population mean. Our online **Confidence Interval Calculator** streamlines this evaluation process.
Mathematical Formula
The confidence interval is calculated by taking the sample mean and adding or subtracting the margin of error, which combines the critical Z-score value, standard deviation, and sample size.
Confidence Interval Formula:
$\text{CI} = \bar{x} \pm \left( z^* \cdot \frac{s}{\sqrt{n}} \right)$
Where: $\bar{x}$ = Sample Mean, $z^*$ = Z-score value, $s$ = Standard deviation, $n$ = Sample size
$\text{CI} = \bar{x} \pm \left( z^* \cdot \frac{s}{\sqrt{n}} \right)$
Where: $\bar{x}$ = Sample Mean, $z^*$ = Z-score value, $s$ = Standard deviation, $n$ = Sample size
Frequently Asked Questions (FAQ)
Q: What does a 95% confidence level actually mean?
A: It means you can be 95% confident that the true population parameter lies within your calculated lower and upper bounds.
A: It means you can be 95% confident that the true population parameter lies within your calculated lower and upper bounds.
Q: How can I narrow my confidence interval width?
A: You can narrow the interval (making your estimate more precise) by increasing your sample size ($n$) or lowering your confidence level.
A: You can narrow the interval (making your estimate more precise) by increasing your sample size ($n$) or lowering your confidence level.
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