Question: To test \(H_{0}: \mu=80\) versus \(H_{1}: \mu \neq 80\), a random sample of size \(n=27\) is obtained from a population that is known to be normally distributed with \(\sigma=8\).

1. If the sample mean is determined to be \(\bar{x}=83.8\), compute the test statistic.
2. If the researcher decides to test this hypothesis at the \(\alpha=0.03\) level of significance, determine the critical value.

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