The U.S. Department of Labor collects data on unemployment insurance payments made to unemployed people in different states. Suppose that during 2011 a random sample of 1000 unemployed people in Florida received an average weekly unemployment benefit of $219.65, while a random sample of 900 unemployed people in Mississippi received an average weekly unemployment benefit of $191.47. Assume that the population standard deviations of 2011 weekly unemployment benefits paid to all unemployed workers in Florida and Mississippi were $35.15 and $28.22, respectively. (A 2011 study by Daily- Finance.com (www.dailyfinance.com/2011/05/12/unemployment-benefits-best-worst-states/) rated Mississippi and Florida as the two worst states for unemployment benefits.)
a. Let µ1 and µ2 be the means of weekly unemployment benefits paid to all unemployed workers during 2011 in Florida and Mississippi, respectively. What is the point estimate of µ1 – µ2?
b. Construct a 96% confidence interval for µ1 – µ2.
c. Using a 2% significance level, can you conclude that the means of all weekly unemployment benefits paid to all unemployed workers during 2011 in Florida and Mississippi are different? Use both the p-value and the critical-value approaches to make this test.