T- distribution

Lecture 18

Similarities between normal distribution & t-distribution

• Both are symmetric & bell-shaped, centered around the mean

• both have a mean of 0 when standardized

• both are used i inferential statistics, particularly for hypothesis testing & confidence interval

Difference between normal distribution & t-distribution

• they’re both symmetrical but t-distribution has heavier tails than normal distribution

• The spread for normal distribution is fixed while the spread for t-distribution depends on the degrees of freedom (df)

When to use Normal Distribution

• the population standard deviation is known

• the sample size is large (n>10), allowing the central limit theorem to be used

when to use t-distribution

• the population deviation is unknown

• The sample size is small (n<10)

• For hypothesis test & confidence interval, involving means with small samples