When to use t-distribution vs normal
- the t distribution should be used when
- the t distribution should be used.whenever quizlet
- the t distribution is used when
- the formula of t distribution is used when
T distribution pdf...
When to use t-distribution vs z distribution
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. 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