The U.S. Bureau of Labor Statistics publishes a variety of unemployment statistics, including the number of individuals who are unemployed and the mean length of weeks that the individuals have been unemployed. For December 2014, the Bureau of Labor Statistics reported the mean length of unemployment was 40.8 weeks. A study on the status of unemployment in City of Chicago with a sample size of 31 unemployed residents shows the average of unemployed length is 44.7 weeks and the sample standard deviation is 5.4 weeks.
a) Find the confidence intervals of the mean length of unemployment for the City of
b) Setup a hypothesis to test whether the length of time in Chicago is longer than national average, and explain the result.