The value of $\beta$ is the area under the bell curve for the distribution of $\bar { x }$ centered at $\mu _ { \mathrm { a } }$ for values of $\bar { x }$ that fall within the acceptance region of the distribution of $\bar { x }$ centered at $\mu _ { 0 }$.

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The acceptance region is the range of values for $\bar { x }$ that are considered acceptable. The area under the bell curve for the distribution of $\bar { x }$ centered at $\mu _ { \mathrm { a } }$ for values of $\bar { x }$ that fall within the acceptance region is the probability that $\bar { x }$ will fall within the acceptance region. This probability is equal to the value of $\beta$.

The Value Of β\betaβ Is the Area Under the Bell Curve for the Distribution

The Value Of $\beta$ Is the Area Under the Bell Curve for the Distribution