T-distribution degrees of freedom

Published Sep 8, 2024

Definition of t-distribution

The t-distribution, also known as Student’s t-distribution, is a probability distribution that arises when estimating the mean of a normally distributed population in situations where the sample size is small, and population standard deviation is unknown.

It plays a crucial role in inferential statistics, particularly in hypothesis testing and constructing confidence intervals when sample sizes are small.

T-distribution vs normal distribution

T distribution mean and variance

T distribution pdf

T distribution table

When do we use t-distribution instead of normal distribution

The t-distribution resembles the normal distribution but has heavier tails, which means it is more prone to producing values far from the mean.

Example

Consider a scenario where a small business wants to estimate the average amount spent by customers in their store.

They collect a sample of the spending amounts from 15 customers. Because the sample size is small and the population standard deviation is unknown, using the t-distribution is appropriate.

*Sample data:*

• Sample Size (n) = 15
• Sample Mean (x̄) = $80
• Sample Standard Deviation (s) = $10

To construct a confidence interval for the population mean, they select

the t distribution is used in statistics when

the t-distribution is just like