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Type I and type II errors
When testing hypothesis (H0) and deciding to either reject or accept a null hypothesis, there are four possible happenings.
a) Acceptance of a true hypothesis as correct decision - accepting the null hypothesis and it occurs to be the correct decision. Note that statistics does not provide absolute information; hence its conclusion could be wrong only that the probability of it being right is high.
b) Rejection of a false hypothesis as correct decision.
c) Rejection of a true hypothesis - (incorrect decision) - it is called type I error, along with probability = α.
d) Acceptance of a false hypothesis - (incorrect decision) - it is called type II error, along with probability = β.
Let Xn be a sequence of distinct real numbers. Defi ne E = {L : L is a subsequential limit of Xn}. Prove E is closed.
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