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[Community Question] Statistics: Calculating a 95% confidence interval for the difference of two random variables

One of our user asked:

Let $ x_1, ..., x_9 $ and $ y_1, ..., y_8 $ be two random samples of two populations. $ \bar x = 7 $ is the mean of the first and $ \bar y = 11 $ the mean of the second sample. The sample standard deviations are $ s_x = 2 $ and $ s_y = 3.5 $. Now I want to calculate a 95% confidence interval for the difference of the mean of the two populations. I know how to calculate a 95% confidence interval for the mean for the populations: $$ \bar x -2*\left(\frac{s_x}{\sqrt 9}\right) $$ and $$ \bar y -2*\left(\frac{s_y}{\sqrt 8}\right) $$ But don't know how to proceed from here.


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