$5.$ Hypothesis Tests $-$ sigma unknown: AOL Time Warner Inc.$\text{'}$s CNN has been the longtime ratings leader of cable television news. Nielsen Media Research indicated that the mean CNN viewing audience was $600,000$ viewers per day during $2002.$ Assume that for a sample of $40$ days during the first half of $2003,$ the daily audience was $612,000$ viewers with a sample standard deviation of $65,000$ viewers. What are the hypotheses if CNN management would like information on any change in the CNN viewing audience? What recommendation would you make to CNN management in this application? Support your answer.