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The result of an Internet poll was reported as evidence that most people believe the pledge of allegiance is constitutional. The poll was conducted by posting a notice on a website and asking people to respond. The results were based on 235 people who responded. Of the 235 people, 172 (73%) believed that the pledge is constitutional, while 63 (27%) believed that the pledge is unconstitutional.
-Assuming the poll had been based on a random sample with a sample size of 235, the reported margin of error of 3%

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Use the following information for questions:
 The result of an Internet poll was reported as evidence that most people believe the pledge of allegiance is constitutional. The poll was conducted by posting a notice on a website and asking people to respond. The results were based on 235 people who responded. Of the 235 people, 172 (73%) believed that the pledge is constitutional, while 63 (27%) believed that the pledge is unconstitutional.
-Assuming the poll had been based on a random sample with a sample size of 235, the reported margin of error of 3%

Quizplus · Accepted Answer

The margin of error for a proportion in a sample of size 235, with a confidence level of approximately 95%, is calculated using the formula for the margin of error in a proportion: $ME = Z \times \sqrt{\frac{p(1-p)}{n}}$, where $Z$ is the Z-score for the desired confidence level (approximately 1.96 for 95%), $p$ is the sample proportion (0.73 in this case), and $n$ is the sample size (235). Plugging in these values, the margin of error is larger than 3% but not as high as 6.5%. However, the actual calculation might not have been provided in the explanation, leading to an incorrect choice. The correct calculation would show a margin of error different from the options provided, but without the exact calculation here, the closest correct theoretical approach based on the information given would suggest a reconsideration of the margin of error, hinting that the provided margin of error in the question might be underestimated due to the nature of the sampling and the size. However, without performing the exact calculation or considering the specific methodology nuances, the response might lean towards recognizing an error in the reported margin without accurately pinpointing its value.

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