Residents of Hawaii have the longest life expectancies in the United States, averaging 81.48 years (www.worldlifeexpectancy.com; data retrieved June 4, 2012).  A sociologist collects data on the age at death for 50 recently deceased Michigan residents.

a. The sociologist believes that the life expectancies of Michigan residents are less than those of Hawaii residents. Specify the competing hypotheses to test this belief.

b. Calculate the value of the test statistic and the p-value.

c. At the 1% significance level, do the data support the sociologist’s belief?