To test \(H_{0}: \mu=50\) versus \(H_{1}: \mu<50\), a simple random sample of size \(n=24\) is obtained from a population that is known to be normally distributed.

(a) If \(\bar{x}=47.1\) and \(s=10.3\), 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 \(t\)-distribution that depicts the critical region.

(d) Will the researcher reject the null hypothesis? Why?