Question: To test Ho: \(\mu \) = 40 versus H₁: \(\mu \) >40, a random sample of size n = 25 is obtained from a population that is known to be normally distributed with \(\sigma \) = 6.

If the sample mean is determined to be \(\bar{X}\) = 42.3, compute the test statistic.

If the researcher decides to test this hypothesis at the \(\alpha \) = 0.1 level of significance, determine the critical value.