## Students T distribution

- We would be t-score and Students t-distribution if the population variance is unknown
- The Students-t distribution is predominantly use for creating confidence intervals and testing hypothesis with normally distributed populations when its sample sizes are small.
- This is particularly useful when we don’t have enough information or it is too costly to obtain it
- All else equal, Student’s T distribution has fatter tails than the Normal distribution and a lower peak. This is to reflect higher level of uncertainity caused by small sample size
- Formula:
- Degrees of freedom: (n-1)
- For calculation, we have t-table Refer Here
- Lets find a confidence interval with 95% confidence for the dataset Refer Here
- To calculate confidence interval when the population variance is unknown we use the following formula
- The result
- Now try to Calculate the CI Intervals with 90% and 99% confidence using Students T distribution
- Margin of Error and Confidence intervals with known & unknown population variances
- Generally t distribution based confidence intervals have larger range due to uncertainity.
- Impact on the range
- CI interval range will be less when the
- Sample size is more
- Sample is not dispersed but rather concentrated => Standard deviation will be less