To test $H_{0}: \mu=50$ versus $H_{1}: \mu<50,$ a random sample of size $n=24$ is obtained from a population that is known to be normally distributed with $\sigma=12$
(a) If the sample mean is determined to be $\bar{x}=47.1$ compute the test statistic.
(b) If the researcher decides to test this hypothesis at the $\alpha=0.05$ level of significance, determine the critical value.
(c) Draw a normal curve that depicts the critical region.
(d) Will the researcher reject the null hypothesis? Why?