Due to the recent economic downturn, Americans have started raiding their already fragile retirement accounts to endure financial hardships such as unemployment, medical emergencies, and buying a home (MSN Money, July 16, 2008). It is reported that between 1998 and 2004, about 12% of families with 401(k) plans borrowed from them. An economist is concerned that this percentage now exceeds 20%. He randomly surveys 190 households with 401(k) plans and finds that 50 are borrowing against them.
a. Set up the null and the alternative hypotheses to test the economist’s concern.
b. Compute the value of the test statistic.
c. Use the p -value approach to test if the economist’s concern is justifiable at α = 0.05.