Super learner
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Resolved: "Completely symmetrical around 0"?
What does this mean? -9.28 to -4.72 does not pass 0. 4.72 to 9.28 also does not pass 0. -4.72 to 4.72 does pass through 0 so why are -9.28, -4.72 & 4.72, 9.28 "completely symmetrical around 0"?
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Super learner
This user is a Super Learner. To become a Super Learner, you need to reach Level 8.
The term "symmetric" refers to the distribution of "x_bar - y_bar" and "y_bar - x_bar".
The distribution of (x_bar - y_bar) has mean 7 and std 1.16; while the distribution of (y_bar - x_bar) has mean -7 and std 1.16. ["x_bar - y_bar" and "y_bar - x_bar" is symmetric about 0]
So for the 95% C.I. of (x_bar - y_bar), we get (-9.28, -4.72). If we want the 95% C.I. of (y_bar - x_bar), then the result would be (4.72, 9.28) [That is, flip the confidence interval along the symmetric line x = 0].
Hope this helps.
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