Social Security payments. The average monthly Social Security benefit for widows and widowers in 2005 was $967 (Statistical Abstract of the United States, U.S. Census Bureau). Payments vary from region to region. In Texas, the 2005 average monthly benefit equaled $940. A social welfare advocate from a rural Texas county be- lieved the 2005 average Social Security benefit for wid- ows and widowers differed significantly from the overall Texas average. To test this assumption, the advocate ran- domly sampled 100 widow/widower monthly benefit payments and found the sample mean = $915 with a standard deviation of $90.
a) Find and interpret a 95% confidence interval estimate for the sample mean 2005 Social Security widow/widower benefit in the rural Texas county.
b) In a hypothesis test performed to determine whether the county's average payment was different, the test was rejected with a P-value = .007 (using the same sample results shown above and a level of significance = .05). Explain how the confidence interval constructed in part a is consistent with the hypothesis test results. Your discussion should include level of confidence, the interval bounds, the P-value, and the hypothesis test decision.