Question 1202239: The city transit authority surveyed 1,000 citizens who regularly use public transportation. Of those surveyed, 658 users said they paid using a monthly subscription as opposed to paying for each ride individually. The margin of error is 2.94%.
Complete the claim that the authors can include in their report.
The transit authority can be 95% confident that the percentage of citizens using public transportation with a monthly subscription is between
% and
%.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the margin of error in this problem was calculated based on the 95% confidence interval.
you use the margin of error to determine the low side of the confidence interval and the high side of the confidence interval.
the low side of the confidence interval is equal to the mean proportion minus the margin of error.
the high side of the confidence interval is equal to the mean proportion plus the margin oferror.
your mean proportion is .658.
the low side of the 95% conficence interval will be .658 - .0294 = .6286.
the high side of the 95% confidence interval will be .658 + .0294 = .6874.
your answer will be that the true proportion is expected to be between .6286 and .6874.
in terms of percent, your answer will be that the true peoportion is expected to be between 62.86% and 68.74%.
that should be your solution.
note that the margin of error calculation is made from the confidence interval.
in this case, you get:
z = (x-m)/s
z is the critical z-score
x is the critical raw score
m is the mean
(x-m) is the margin of error)
s is the standard error.
at 95% confidence interval, the critical z-score is plus or minus 1.96.
the standard error is equal to sqrt(p * q / 1000) = sqrt(.658 * .342 / 1000) = .015 rounded to 2 decimal places.
the critical z-score formula becomes:
1.96 = (x-m) / .015
solve for (x-m) to get:
(x-m) = 1.96 * .015 = .0294.
(x-m) is the margin of error and it is equal to .0294.
this is the same as the margin of error that was already given.
let me know if you have any quetions.
theo
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