## 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

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