Question

please write the formula for t-distribution

Answer 1

T-DISTRIBUTION FORMULA

In probability and statistics, the t-distribution is any member of a family of continuous probability distributions 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.

According to the central limit theorem, the sampling distribution of a statistic will follow a normal distribution, as long as the sample size is sufficiently large.

Therefore, when we know the standard deviation of the population, we can compute a z-score, and use the normal distribution to evaluate probabilities with the sample mean.

The t-distribution with degrees of freedom “n – 1” is given below.

t=x¯¯¯−μsN−−√