Question

what is the formula for a 2 sample T-test with

what each letter or symbol in the equation is?

Answer 1

two sample t test used for the testing of the two samples of the mean :

it is used when we do not know population variance or population variance is unknown .

her we can assume equal variance and unequal variance .

Assuming equal variances,

the test statistic is t calculated as: -

where x bar 1 and x bar 2 are the sample means,

s1^2 = Σ ( x – xbar 1 )² / ( n1 – 1 ) ## variance for first sample

s2 ^2 = Σ ( x – xbar 2 )² / ( n2 – 1 ) ## variance for second sample

s² is the pooled sample variance,  

n₁ and n₂ are the sample sizes

and t is a Student t quantile with n₁ + n₂ - 2 degrees of freedom.

## if variance is not equal then there is formula for degree of freedom :