If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Simulation showing value of t statistic

See why we use t statistics when building confidence intervals for a mean using the sample standard deviation in place of the population standard deviation.

## Want to join the conversation?

• How can I get this simulation?
• Why we have to use the t table to calculate the confidence interval of the mean but the z table to the proportion? Is there any difference?
• when using "z with s", we have got a hit rate of approx 92%, which is not that much different to the hit rate of 95% when using "z with sigma", so is the difference really significant?
• Okay, so is there an intuitive explanation why it is better to use T-statistic instead of Z? I have been thinking about this for a long time because I cannot recall this being explained at my lectures. If you have some neat answer for this, please share!
• I think it's that because you have to account for the variability of the sample standard deviation, which the t-model accounts for by having wider tails, which increases the confidence interval, which kind of makes sense because there is more variability from having less samples.