SOLUTION: 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 explosives h
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Question 1026706: 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 explosives 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 5-6, 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 will 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 α = 0.05.
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 sensitive decision, use α = 0.01. What is your recommendation?
Answers:
Ho: p ≤ 0.80
Ha: p > 0.80
Conclude that airline travelers feel security will be improved
b) Cannot reject Ho; mandatory use is not recommended
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
On January 5-6, 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 will 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 α = 0.05.
Ho: p <= 0.8
Ha: p > 0.8 (claim)
sample proportion:: 423/455 = 0.84
z(0.84) = (0.84-0.80)/sqrt[0.8*0.2/542] = 2.3281
p-value = P(z > 2.3281) = normalcdf(2.3281,100) = 0.0099
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Since the p-value is less than 5%, reject Ho.
The test results support the claim that p > 80%
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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 sensitive decision, use α = 0.01. What is your recommendation?
Since the p-value rounds to 1% you should do more testing
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Cheers,
Stan H.
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