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4. Suppose that $X_1, X_2, dots, X_n$ form a random sample from a normal distribution with unknown mean $mu$ and known variance $sigma^2$. At the level of $alpha$, we are interested in testing the hypotheses $H_0: mu = mu_0$ vs. $H_1: mu eq mu_0$. Show that the likelihood ratio test is equivalent to a z-test.

          4. Suppose that $X_1, X_2, dots, X_n$ form a random sample from a normal distribution with unknown mean $mu$ and known variance $sigma^2$. At the level of $alpha$, we are interested in testing the hypotheses

$H_0: mu = mu_0$ vs. $H_1: mu 
eq mu_0$.

Show that the likelihood ratio test is equivalent to a z-test.

4. Suppose that X1, X2, dots, Xn form a random sample from a normal distribution with unknown mean mu and known variance sigma^2. At the level of alpha, we are interested in testing the hypotheses

H0: mu = mu0 vs. H1: mu
eq mu0.

Show that the likelihood ratio test is equivalent to a z-test.

Added by Nancy M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Ameer Said

01/09/2022

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Suppose that X1, X2, ..., Xn form a random sample from a normal distribution with unknown mean μ and known variance σ^2. At the level of α, we are interested in testing the hypotheses: H0: μ = μ0 vs. H1: μ ≠ μ0. Show that the likelihood ratio test is equivalent to a z-test.