Consider a test of $\mathrm { H } _ { 0 } : \mu = 4$. For the following case, give the rejection region for the test in terms of the $z$-statistic: $\mathrm { H } _ { \mathrm { a } } : \mu \neq 4 , \alpha = 0.01$
A) $z 2.575$
B) $| z | 2.33$
C) $z 2.33$
D) $| z | 2.575$

Question

Consider a test of $\mathrm { H } _ { 0 } : \mu = 4$. For the following case, give the rejection region for the test in terms of the $z$-statistic: $\mathrm { H } _ { \mathrm { a } } : \mu \neq 4 , \alpha = 0.01$
A) $z > 2.575$
B) $| z | > 2.33$
C) $z > 2.33$
D) $| z | > 2.575$

Quizplus · Accepted Answer

Since the alternative hypothesis is $\mu \neq 4$, this is a two-tailed test. For a significance level of $\alpha = 0.01$, the critical z-values for a two-tailed test are $\pm 2.575$, indicating rejection regions in both tails of the distribution.

Consider a Test Of H0:μ=4\mathrm { H } _ { 0 } : \mu = 4H0​:μ=4

Consider a Test Of $\mathrm { H } _ { 0 } : \mu = 4$