Suppose you are interested in the average Hourly Rate for all 59,408 employees of the State of Ohio in 2014. Assume that the standard deviation of Hourly Rate for all employees of the State of Ohio in 2014 is known to be $8.94. You take a random sample of 200 employees and find that the average hourly wage is $29.27.
1. Estimate the true average Hourly Rate for all State of Ohio employees in 2014 using your sample. Provide a summary of ALL the steps you used to find your answer, then give your answer as a complete sentence, rounding all numbers in your final answer to TWO decimal places and using appropriate units.
2. A news report on NPR declared that the average hourly rate for 2014 was $30.56. You believe, based on your analysis from the case studies, that the average hourly wage is different than what was reported on the radio. Perform an appropriate hypothesis test, based on your sample of 200 employees, to decide if there enough evidence to support your intuition.