The U.S. Department of Labor collects data on unemployment insurance payments. Suppose that during 2009 a random sample of 80 unemployed people in Alabama received an average weekly benefit of $201.85, whereas a random sample of 65 unemployed people in Mississippi received an average weekly benefit of $185.31. Assume that the population standard deviations of all weekly unemployment benefits in Alabama and Mississippi are $32.48 and $26.15, respectively. Using the 4% significance level, can you conclude that the means of all weekly unemployment benefits in Alabama and Mississippi paid during 2009 are different?

Question

The U.S. Department of Labor collects data on unemployment insurance payments. Suppose that during 2009 a random sample of 80 unemployed people in Alabama received an average weekly benefit of $201.85, whereas a random sample of 65 unemployed people in Mississippi received an average weekly benefit of $185.31. Assume that the population standard deviations of all weekly unemployment benefits in Alabama and Mississippi are $32.48 and $26.15, respectively. Using the 4% significance level, can you conclude that the means of all weekly unemployment benefits in Alabama and Mississippi paid during 2009 are different?

Answer 1

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability.

I'll let you do the calculations.