On December $25,2009,$ an airline passenger was subdued while attempting to blow up a Northwest Airlines flight headed for Detroit, Michigan. The passenger had smuggled explo$-$ sives hidden in his underwear past a metal detector at an airport screening facility. As a result, the Transportation Security Administration $($TSA$)$ proposed installing full$-$body scanners to replace the metal detectors at the nation$$s largest airports. This proposal resulted in strong objections from privacy advocates who considered the scanners an invasion of privacy. On January $56,2010,$ USA Today conducted a poll of $542$ adults to learn what proportion of airline travelers approved of using full$-$body scanners $($USA Today, January $11,2010).$ The poll results showed that $455$ of the respondents felt that full$-$body scanners would improve airline security and $423$ indicated that they approved of using the devices.

a$.$ Conduct a hypothesis test to determine if the results of the poll justify concluding

that over $80\%$ of airline travelers feel that the use of full$-$body scanners will improve

airline security. Use # $=\mathrm{.}05.$

b$.$ Suppose the TSA will go forward with the installation and mandatory use of full$-$body

scanners if over $75\%$ of airline travelers approve of using the devices. You have been told to conduct a statistical analysis using the poll results to determine if the TSA should require mandatory use of the full$-$body scanners. Because this is viewed as a very sensi$-$ tive decision, use # $=\mathrm{.}01.$ What is your recommendation?