After the 2010 earthquake in Haiti, many charitable organizations conducted fundraising campaigns to raise money for emergency relief. Some of these cam- paigns allowed people to donate by sending a text mes- sage using a cell phone to have the donated amount added to their cell-phone bill. The report "Early Signals on Mobile Philanthropy: Is Haiti the Tipping Point?" (Edge Research, 2010) describes the results of a national survey of 1526 people that investigated the ways in which people made donations to the Haiti relief effort. The report states that 17% of Gen Y respondents (those born between 1980 and 1988) and 14% of Gen X re- spondents (those born between 1968 and 1979) said that they had made a donation to the Haiti relief effort via text message. The percentage making a donation via text message was much lower for older respondents. The re- port did not say how many respondents were in the Gen Y and Gen X samples, but for purposes of this exercise, suppose that both sample sizes were 400 and that it is reasonable to regard the samples as representative of the Gen Y and Gen X populations.
a. Is there convincing evidence that the proportion of those in Gen Y who donated to Haiti relief via text message is greater than the proportion for Gen X? Use CY = .01.
b. Estimate the difference between the proportion of Gen Y and the proportion of Gen X that made a donation via text message using a 99% confidence inter- val. Provide an interpretation of both the interval and the associated confidence level.