
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
A) For a sample of size $n$ taken from a normal population with a known standard deviation $\sigma$, the sample mean $\bar{x}$ is found. At a significance level $\alpha$, it is required to find the power function of the test of the null hypothesis $H_{0}: a=a_{0}$ regarding the population mean $a$ with the hypothetical value $a_{0}$, under the competing hypothesis $H_{1}: a=a_{1} \neq a_{0}$.

B) For a sample of size $n=16$ taken from a normal population with a known standard deviation $\sigma=5$, at a significance level of 0.05, the null hypothesis $H_{0}: a=a_{0}=20$ regarding the population mean $a$ with the hypothetical value $a_{0}=20$ is tested against the competing hypothesis $H_{1}: a \neq 20$. Calculate the power of the two-sided test for the hypothesized value of the population mean $a_{1}=24$.

Present the answer in LaTex format: \boxed{Your answer}
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