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Assume that X has a normal distribution with unknown mean and variance 25 . We shall test H0:= 60 against H1:<60. Let the critical region be defined by C= {X:X<57} where X is the sample mean of a random sample of size n=20 from this distribution. (i) What is the significance level of the test? (ii) Find the probability of Type II error if =55..

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Assume that X has a normal distribution with unknown mean and variance 25 . We shall test H0:= 60 against H1:<60. Let the critical region be defined by C= {X:X<57} where X is the sample mean of a random sample of size n=20 from this distribution. (i) What is the significance level of the test? (ii) Find the probability of Type II error if =55.

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  • 1. Assume that X has a normal distribution with unknown mean and variance 25 . We shall test H0:= 60 against H1:<60. Let the critical region be defined by C= {X:X<57} where X is the sample mean of a random sample of size n=20 from this distribution. (i) What is the significance level of the test? (ii) Find the probability of Type II error if =55.