The U.S. Department of Labor gathers data on unemployment insurance payments. Assume that throughout 2009 a random sample of 70 unemployed people in Alabama received average weekly benefit of $199.65, whereas a random sample of 65 unemployed people in Mississippi received average weekly benefit of $187.93. Suppose that the population standard deviations of all weekly unemployment benefits in Alabama and Mississippi are $32.48 and $26.15, respectively,
a. Let µ1 and µ2 be the means of all weekly unemployment benefits in Alabama and Mississippi paid throughout 2009, respectively. Determine the point estimate of µ1, - µ2?
b. Develop a 96% confidence interval for µ1 - µ2
c. Using the 4% significance level, can you conclude that means of all weekly unemployment benefits in Alabama and Mississippi paid during 2009 are different? Employ both approaches to make this test.