Question

Do you know what GOP stands for? It is not a trick question, though appar- ently it is a tricky question for the majority of Americans. In a 60 Minutes Vanity Fair poll just 45 percent correctly answered a multiple- choice question about the meaning of the widely used acronym for the Repub- lican Party. (For the record, it stands for "Grand Old Party.") More than a third guessed "Government of the People," while a few jokesters (one hopes) opted for "Grumpy Old People", "Gods Own Party", or "Gauntlet of Power". Fewer than one in 10 had the modesty to select "Dont know". Members of the GOP were marginally more likely to know what it stands for, with 51 percent of Republicans getting the right answer. Just 38 percent of Democrats got it right, though that may be partly because 9 percent of them opted for "Grumpy Old People". L... 11 The poll was based on a random sample of 1,165 adults across the country, with a margin of error of plus or minus 3 percent. (a) Using information in the text, recalculate the poll's margin of error. (b) What is wrong with the estimated margin of error as described in the text?

Answer 1

The Margin of Error is calculated using the following formula:

Margin of Error = zx P x (1 - p) / V

Suppose confidence level (α) of 95%

z = 1.96 for α = 95%

p = proportion percentage = 45%

n = sample size = 1165

z = 1.96, p = 0.45, n = 1165

Margin of Error = 1.96 × 0.45 × (1 - 0.45) / 1165

Margin of Error = 0.975 / 34.132 × 100 = 2.857%

The margin of error is ±2.857%