Under the assumption that $\mu = \mu _ { \mathrm { a } }$, where $\mu _ { \mathrm { a } }$ is the alternative mean, the distribution of $\bar { x }$ is mound shaped and symmetric about $\mu _ { \mathrm { a } }$.

Question

Quizplus · Accepted Answer

When assuming $\mu = \mu_a$, the distribution of the sample mean $\bar{x}$ is centered around the alternative mean $\mu_a$, and if the underlying population distribution is normal or the sample size is large enough (Central Limit Theorem), the distribution of $\bar{x}$ will be mound-shaped (normal) and symmetric about $\mu_a$.

Under the Assumption That μ=μa\mu = \mu _ { \mathrm { a } }μ=μa​

Under the Assumption That $\mu = \mu _ { \mathrm { a } }$