For Problems #1 through #9, consider the following information: Palisades University Medical Center is making a concerted effort to improve salaries for its hourly employees working in the hospital's low skill labor force. According to a recent though possibly premature press release from the human resources department, for this population, the (mean) average hourly wages for these workers is now $20, give or take $2, which represents the population standard deviation. Stacy the stats intern working in the chief operations officer collected a sample of the hourly wages for 36 such low skills workers, and found they had a sample mean hourly wage of $19. She is admittedly skeptical that the reported wages are at the reported level, though respectfully won't speculate if higher or lower than reported. Is the human resources department's claim reasonable, at the 1% level of significance? #1:What are the null and alternative hypotheses, stated concisely with proper symbols? #2:What type of hypothesis test is involved: two-tail, one-tail left, or one-tail right? Explain. #3:Which type of test statistic is generated (i.e., z or t) and why? Explain. #4:Determine the critical value(s) that designate the rejection region(s). #5:Determine the value of the test statistic (i.e., z or t). #6:Determine the p-value that corresponds to the test statistic. #7:Concisely state the technical conclusion using appropriate and complete statistical language. #8:Interpret the findings in complete thoughts/phrases and within the context of the problem. #9:Construct the corresponding confidence interval which affirms the conclusion