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# 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?
• The difference lies in the formulas used for calculating confidence intervals for the mean and the proportion. For estimating the population mean, we typically use the t-distribution when the population standard deviation is unknown, as it accounts for the variability introduced by using the sample standard deviation. For estimating the population proportion, we use the normal distribution (z-table) because the formula for the standard error of the sample proportion does not involve the population standard deviation.
(1 vote)
• If using a T-table and a sample standard deviation is always preferable over using a Z-table and the sample standard deviation then why even teach the method using the z-table?
• T tables are better for smaller sample sizes. If N is over 30, it's better to use Z table.
(1 vote)
• 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?
• While the difference between a hit rate of approximately 92% and a desired rate of 95% may not seem significant at first glance, in statistical inference, even small differences in accuracy can have practical implications, especially when making decisions based on the results. Achieving the desired confidence level is important to ensure the reliability of the inference made from the sample data.
(1 vote)
• 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.
• How can we find and experiment with this simulation?