Question

Elderly drivers. 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.9

(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?

Answer 1

Solution:

Given:

Sample size= n = 1018

Sample proportion =

Margin of Error = 3% = 0.03

confidence level = 95% = 0.95

Part a) Verify the margin of error reported by The Marist Poll.

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Thus

Yes the margin of error reported by The Marist Poll is correct.

Part 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?

Find a 95% confidence interval for proportion:

Since both the limits of confidence interval are less than 70%, the poll DOES NOT 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