The second normal population variance is the same but the unknown is the hypothesis test for the mean difference - online calculation tool

Suppose the two populations X and Y are independent of each other and obey the normal distribution. The mean and variance of X areμ₁,σ₁², The mean and variance of Y areμ₂,σ₂², that is X~N(μ₁,σ₁²), Y~N(μ₂,σ₂²),This page is σ₁²,σ₂²which are same but unknown mean differenceμ₁-μ₂make hypothesis test，the statistics are

， among them

,n₁,X,S₁ are the sample size, sample mean, and sample standard deviation of the population X. n₂,Y,S₂are the sample size, sample mean, and sample standard deviation of the overall Y.