According to a new Health of Boston report, female residents in Boston have a higher average life expectancy as compared to male residents (The Boston Globe, August 16, 2010). You collect the following sample data to verify the results of the report. You also use the historical standard deviation of 8.2 years for females and 8.6 years for males.

FemaleMale

1 = 81.1 years ...
2 = 74.8 years

n1 = 32 .......n2 = 32

a. Set up the hypotheses to test whether the average life expectancy of female Bostonians is higher than that of male Bostonians.

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

c. At the 10% significance level, what is the conclusion? On average, do female Bostonians live longer than male Bostonians?

d. Repeat the hypothesis test using the critical value approach.