※ 引述《alanfirst ()》之銘言：
: 3. Suppose we plan to select a random sample from a normal distribution
: known to have a standard deviation of 8. We know that the population mean is
: either 42 or 50, and we wish to test Ho:u=42 against H1=50 determine the sample
: size n and a critical region such that α=0.05 and B=0.1
_
Suppose we have X1,.....Xn,from LR-test we know Xn is our test statistic,
and the critical region can be define using the relation that α=0.05
_
Xn-42
=> P( -------> c )=0.05 => c=(8/n)*Z0.05+42 --------(A)
8/n
next, we use B=0.1 to determine the sample size n
_
Xn-50 c-50 c-50
=> P( --------- < ---------)=0.1 => ---------=-Z0.1 -------(B)
8/n 8/n 8/n
using formula A and B, we can solve the problem.
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