35. 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 believed the 2005 average Social Security benefit for widows and widowers differed significantly from the overall Texas average. To test this assumption, the advocate randomly 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.