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I was taught in class today that a 25% CI requires that the critical value in the error term comes from a t-distribution with 23 degrees of freedom? I am unsure as to why this is?

~For example, Lets use this. . .

Average length of workweeks of 15 randomly selected employees in the mining industry and 10 randomly selected employees in the manufacturing industry were obtained.

Miners(x)=15 observation, Mean of 47.5, and Std. Dev. of 5.5

Manufacturers= 10 observations, Mean of 42.5, and Std. Dev of 4.9.

With this data I obtained that Sp 5.27, t=2.069, and a 95% CI =(0.55,9.45)

~I never used 23 degrees of freedom to obtain those answers, were are correct. Why should the 95% CI for the difference between x-y require the critical value in the error term comes from a t-distribtuion with 23 degrees of freedom?