4. In January 2011, The Marist Poll published a report stating that 66% of adult

Question

4. In January 2011, The Marist Poll published a report stating that 66% of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age. It was also reported that interviews were conducted on 1,018 American adults, and that the margin of error was 3% using a 95% confidence level. (a) Verify the margin of error reported by The Marist Poll. (b) Based on a 95% confidence interval, does the poll provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65? (c ) Is it possible that true proportion of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age is 70% If so, how likely it is?

Explanation / Answer

sample size n = 1018

sample proportion = p = 0.66

standard error of proportion = sqrt(0.66 * 0.34/1018) = 0.01485

(b) Here 95% confidence interval = p^ +- MOE

= 0.66 +- 0.03

= (0.63, 0.69)

so poll doesn't provide convincing evidence that more thn 70% of the population think that licensed drivers should be required to retake their road test they turn 65.

(c) Yes, it is possible that true proportion of adults is 70%,

Pr(p^ >0.7) = NORM(p^ > 0.7 ; 0.66 ; 0.01485)

Z = (0.7 - 0.66)/0.01485 = 2.6936

Pr(p^ >0.7) = NORM(p^ > 0.7 ; 0.66 ; 0.01485) = Pr(Z > 2.6936) = 1 - 0.9964 = 0.0036

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