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The number of milliliters in a bottle of cough medicine is normally distributed with mean μ...

The number of milliliters in a bottle of cough medicine is normally distributed with mean μ = 350 ml and standard deviation σ = 3. A new bottling procedure is introduced, and a random sample of 144 bottles has sample mean x ¯ = 351 ml. it is assumed that the standard deviation is still 3 ml. The null hypothesis is H 0: μ = 350, the alternative hypothesis is H a: μ > 350. and the level of significance is α = 0.05.

(a) What is the critical region for the standard normal Z and for the sample mean X ¯?

(b) What is the probability of rejecting H 0, given that H 0 is true (Type I error)?

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