Depression engulfs millions of Americans every day. A new federal study reported that 10.9% of adults aged 18–24 identified with some level of depression versus 6.8% of adults aged 65 or older (Boston Globe, October 18, 2010). Suppose 250 young adults (18–24 years old) and
200 older adults (65 years old and older) responded to the study.
a. Develop the appropriate null and alternative hypotheses to test whether the proportion of young adults suffering from depression is greater than the proportion of older adults suffering from depression.
b. Calculate the value of the test statistic and the p-value.
c. At the 5% significance level, what is the conclusion? Do the sample data suggest that young adults suffer more from depression than older adults?