# Question

Let X equal the number of milliliters of a liquid in a bottle that has a label volume of 350 ml. Assume that the distribution of X is N(μ, 4). To test the null hypothesis H0: μ = 355 against the alternative hypothesis H1: μ < 355, let the critical region be defined by C = {x : x ≤ 354.05}, here x is the sample mean of the contents of a random sample of n = 12 bottles.

(a) Find the power function K(μ) for this test.

(b) What is the (approximate) significance level of the test?

(c) Find the values of K(354.05) and K(353.1), and sketch the graph of the power function.

(d) Use the following 12 observations to state your conclusion from this test:

(a) Find the power function K(μ) for this test.

(b) What is the (approximate) significance level of the test?

(c) Find the values of K(354.05) and K(353.1), and sketch the graph of the power function.

(d) Use the following 12 observations to state your conclusion from this test:

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