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Unformatted text preview: the 6 The distribution of ̅ is: 0 X n 0 z But suppose the true is to the right of . Then the true distribution of ̅ is
say: 0 0 z n The shaded area in the above diagram gives the probability of correctly
rejecting H0 (i.e. the power, 1- which is greater than )
Now suppose the sample size is increased. As a result:
̅ decreases & hence √ decreases. Suppose the new sample size is n1>n. 7 The distribution of ̅ will now look something like: 0 0 z n1 X Note that with a fixed the rejection region cutoff is now smaller. Again, if the
true is actually to the right of , the probability of rejecting the same
incorrect null hypothesis is higher than before. Diagrammatically the true
distribution of ̅ will be say 0 z
n1 0 X Again the shaded area in the above diagram gives the probability of correctly
Conclusion: The probability of correctly rejecting a false H0. (the power of the
test, as discussed in lectures this week) increases as n increases given we keep
the Type I error () fixed.
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