The student newspaper runs a weekly question that readers can answer online or by campus mail. One question was "Do you think the college is doing enough to provide student parking?" Of the 100 people who responded, 79% said "No".What is the 95% Confidence Interval?Group of answer choices95%+/-7.9%100+/-7979%+/-5%79%+/-10%
Question
The student newspaper runs a weekly question that readers can answer online or by campus mail. One question was "Do you think the college is doing enough to provide student parking?" Of the 100 people who responded, 79% said "No".What is the 95% Confidence Interval?Group of answer choices95%+/-7.9%100+/-7979%+/-5%79%+/-10%
Solution
To calculate the 95% confidence interval, we first need to find the standard error.
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First, calculate the proportion of "No" responses, which is 79% or 0.79.
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Then, calculate the proportion of "Yes" responses, which is 100% - 79% = 21% or 0.21.
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The formula for standard error (SE) for a proportion is sqrt[p(1-p)/n], where p is the proportion (in this case, 0.79), and n is the total number of responses (in this case, 100).
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So, SE = sqrt[0.79 * 0.21 / 100] = 0.040.
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The 95% confidence interval is typically calculated as the proportion ± 1.96*SE.
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So, the 95% confidence interval would be 0.79 ± 1.96*0.040 = 0.79 ± 0.0784.
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Convert this back to percentages, we get 79% ± 7.84%.
So, the closest answer choice would be 79% +/- 7.9%.
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