36. Social Security payments, part 2. In a neighboring county, a newspaper wrote that widow/widower Social Security benefits were significantly lower in the county than in all the other counties of Texas. The newspaper reported that the average 2005 monthly benefit for widows and widowers was $900, based on a random sample of 100 with standard deviation of $90.

a) Find and interpret a 95% confidence interval estimate for the sample mean Social Security widow/widower benefit in this county.

b) Is this county’s average widow/widower benefit different from the Texas average of $940?