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

(a) If the sample standard deviation is determined to be \(s=47.2\), 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 chi-square distribution and depict the critical region.

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