The global recession has led more and more people to move in with relatives, which has resulted in a large number of multigenerational households. An October 2011 Pew Research Center poll showed that 11.5% of people living in multigenerational households were living below the poverty level, and 14.6% of people living in other types of households were living below the poverty level (www.pewsocialtrends.org/2011/10/03/fighting-poverty-in-a-bad-economy-americans-move-in-with-relatives/? src-prc-headline). Suppose that these results were based on samples of 1000 people living in multigenerational households and 2000 people living in other types of households.
a. Let p1 be the proportion of all people in multigenerational households who live below the poverty level and p2 be the proportion of all people in other types of households who live below the poverty level. Construct a 98% confidence interval for p1 – p2.
b. Using a 2.5% significance level, can you conclude that p1 is less than p2? Use the critical-value approach.
c. Repeat part b using the p-value approach.