A Large University Is Interested in Learning About the Average $23.243$

A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 51 students and asked each to provide the amount of time they spent traveling to campus. The sample results found that the sample mean was $23.243$ minutes and the sample standard deviation was $20.40$ minutes. Find the rejection region for determining if the population standard deviation exceeds 20 minutes. Use $\alpha = 0.05$ .

A) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 34.7642$
B) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 71.4202$
C) Reject $\mathrm { H } _ { 0 }$ if $\mathrm { z } > 1.645$
D) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 67.5048$