# Question

Assume that the weight X in ounces of a “10- ounce” box of cornflakes is N(μ, 0.03). Let X1, X2, . . . , Xn be a random sample from this distribution.

(a) To test the hypothesis H0: μ ≥ 10.35 against the alternative hypothesis H1: μ < 10.35, what is the critical region of size α = 0.05 specified by the likelihood ratio test criterion?

(b) If a random sample of n = 50 boxes yielded a sample mean of = 10.31, is H0 rejected?

(c) What is the p-value of this test?

(a) To test the hypothesis H0: μ ≥ 10.35 against the alternative hypothesis H1: μ < 10.35, what is the critical region of size α = 0.05 specified by the likelihood ratio test criterion?

(b) If a random sample of n = 50 boxes yielded a sample mean of = 10.31, is H0 rejected?

(c) What is the p-value of this test?

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