A research firm conducts a sample survey and discovers that, of all the new watchers of three-dimensional tv, 77% have not reported any side effects such as vertigo, headache, or undue eyestrain compared with watching regular television. if this sample questionnaire had 2,100 respondents, what is the margin of error (me), rounded to the nearest thousandth? hint: me equals plus or minus two times square root of start fraction p hat left parenthesis one minus p hat right parenthesis over n end fraction end square root comma where p hat is the yes proportion in the sample and n is the sample size. me = ±0.009 me = ±0.017 me = ±0.018 me = ±1.837

Question

Mathematics

Marley Kirk

5 December, 07:41

A research firm conducts a sample survey and discovers that, of all the new watchers of three-dimensional tv, 77% have not reported any side effects such as vertigo, headache, or undue eyestrain compared with watching regular television. if this sample questionnaire had 2,100 respondents, what is the margin of error (me), rounded to the nearest thousandth? hint: me equals plus or minus two times square root of start fraction p hat left parenthesis one minus p hat right parenthesis over n end fraction end square root comma where p hat is the yes proportion in the sample and n is the sample size. me = ±0.009 me = ±0.017 me = ±0.018 me = ±1.837

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Answers (1)

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Quentin Howard · Answer 1

Answer: + / - 0.018

All you have to do is plug the known values into the equation and evaluate it.

First, do the work under the square root sign. 0.77 (1-0.77) / 2100 gives you a very small number. If you take the square root of that, you will have 0.0091.

The last step is to just multiply that by 2 and you will have 0.018