The random variable x has a normal distribution with standard deviation 3 5 but unknown mean The hypothesis H 0 3 is to be tested against H 1 4 by taking a random sample of size 70 from the distribution of x and rejecting H 0 if the sample mean exceeds 3 2 a ) Find the Type I error probability of this procedure, to two decimal places b ) Find the Type II error probability of this procedure, to two decimal places

Question: The random variable x has a normal distribution with standard deviation 3.5 but unknown mean . The hypothesis H 0 : = 3 is to

The random variable x has a normal distribution with standard deviation 3.5 but unknown mean . The hypothesis H₀ : = 3 is to be tested against H₁ : = 4 by taking a random sample of size 70 from the distribution of x and rejecting H₀ if the sample mean exceeds 3.2 .

a ) Find the Type I error probability of this procedure, to two decimal places:

b ) Find the Type II error probability of this procedure, to two decimal places:

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