9.54 Authors of the news release titled “Major Gaps Still Exist Between the Perception and the Reality of Americans’ Internet Security Protections, Study Finds”

(The National Cyber Security Alliance) estimated the proportion of Americans who claim to have a firewall installed on their computer to protect them from computer hackers to be .80 based on a survey conducted by the Zogby market research firm. They also estimated the proportion of those who actually have a firewall installed to be .42, based on checkups performed by Norton’s PC Help software. The following quote is from the news release:

For the study, NCSA commissioned a Zogby survey of more than 3000 Americans and Symantec conducted checkups of 400 Americans’ personal computers performed by PC Help by Norton (www.norton.com/tuneup). The Zogby poll has a margin of error of 1/2 1.6% and the checkup has a margin of error of 1/2 5%.

Explain why the margins of error for the two estimated proportions are different.