QUESTION 3 t Distribution (17 points) A researcher examines trends in hourly earnings in the US of working college graduates, ages 25 to 34. The annual average hourly earnings from 2010 to 2015 is recorded as follows. (The design of the study justifies the assumptions that the sample can be treated as a simple random sample). Year 2010 2011 2012 2013 2014 2015 Earnings 22.3 23.5 25.9 24.1 24.9 26.4 (a) (3 points) Use the sample data to construct a 98% confidence interval estimate of, the average hourly earnings of the period 2010-2015. Use Table C. (b) (2 points) What does the confidence interval suggest? (c) (12 points) A group of economists claim that the true average hourly wage is $24. (c.1) Conduct an appropriate hypothesis testing (explain what you are testing) and make your conclusions by (c.2) calculating a t-statistic. (c.3) Use Table C to make your decisions around the hypotheses. (c.4) Does your sample provide good evidence that, on average, the true average hourly wage is indeed $24? Clearly explain all your notations