TATITIC CALCULATOR
Mad
A precise tool.
What is the Mad & How does it work?
A confidence interval provides a range of plausible values for an unknown population parameter based on sample data.
When the population standard deviation (sigma) is known, the interval for the population mean (mu) is calculated using the Z‑distribution.
\bar{x} pm z_{\alpha/2} frac{\sigma}{\sqrt{n}}
\bar{x} = sample mean, z_{\alpha/2} = critical Z‑value, \sigma = population standard deviation, n = sample size
The resulting lower and upper bounds indicate that, with the chosen confidence level, the true mean lies within this interval.
Parameters
Result
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Frequently Asked Questions
What is a confidence interval?
A confidence interval provides a range of plausible values for an unknown population parameter based on sample data.
When should I use the Z-distribution to calculate a confidence interval?
You should use the Z-distribution when the population standard deviation is known and the sample size is large enough (typically n > 30).
How do I interpret the lower and upper bounds of a confidence interval?
The lower and upper bounds indicate that, with the chosen confidence level, the true population parameter lies within this range.
What is the formula for calculating a confidence interval using the Z-distribution?
The formula is bar{x} ± z_{alpha/2} * (sigma / √n), where bar{x} is the sample mean, z_{alpha/2} is the critical Z-value, sigma is the population standard deviation, and n is the sample size.
How does changing the confidence level affect the width of the confidence interval?
Increasing the confidence level results in a wider confidence interval because it requires a greater degree of certainty that the true parameter falls within the range.
What is the difference between a population standard deviation and a sample standard deviation?
A population standard deviation (sigma) describes the variability of all members in a population, while a sample standard deviation (s) estimates this variability from a subset of the population.
Can I use this calculator if my sample size is small and the population standard deviation is unknown?
No, for small samples with an unknown population standard deviation, you should use the t-distribution instead.
Results are for informational purposes only and do not constitute professional advice.