This simulation allows you to explore the concept of confidence intervals in statistics. You'll discover how statistical confidence works in practice by:
A confidence interval is a range of values that provides an estimate of an unknown population parameter with a specified level of confidence. It helps quantify the uncertainty in sample estimates and provides a range of plausible values for the true population parameter.
Misconception: A 95% confidence interval means there is a 95% probability that the true parameter lies within the interval.
Reality: The confidence level (95%) refers to the procedure's reliability, not the probability of the parameter being in any specific interval. If we were to repeat the sampling process many times, about 95% of the resulting intervals would contain the true parameter.
The probability (typically expressed as a percentage) that the confidence interval contains the true population parameter. Common levels are 90%, 95%, and 99%.
The distance between the point estimate and the confidence interval bounds, calculated as:
The proportion of intervals that contain the true population parameter when the process is repeated many times. Should match the confidence level.
Larger sample sizes () lead to narrower confidence intervals, providing more precise estimates of the population parameter.
For a population mean with known standard deviation:
Where:
This simulation allows you to explore the concept of confidence intervals in statistics. You'll discover how statistical confidence works in practice by:
A confidence interval is a range of values that provides an estimate of an unknown population parameter with a specified level of confidence. It helps quantify the uncertainty in sample estimates and provides a range of plausible values for the true population parameter.
Misconception: A 95% confidence interval means there is a 95% probability that the true parameter lies within the interval.
Reality: The confidence level (95%) refers to the procedure's reliability, not the probability of the parameter being in any specific interval. If we were to repeat the sampling process many times, about 95% of the resulting intervals would contain the true parameter.
The probability (typically expressed as a percentage) that the confidence interval contains the true population parameter. Common levels are 90%, 95%, and 99%.
The distance between the point estimate and the confidence interval bounds, calculated as:
The proportion of intervals that contain the true population parameter when the process is repeated many times. Should match the confidence level.
Larger sample sizes () lead to narrower confidence intervals, providing more precise estimates of the population parameter.
For a population mean with known standard deviation:
Where:
