A researcher has conducted a survey using a simple random sample of 50 licensed drivers to create a confidence interval to estimate the proportion of licensed drivers favoring the construction of a new stoplight. Assume that the sample proportion does not change. The researcher now decides to survey a random sample of 200 people instead of 50 licensed drivers. Which of the following statements best describes how the confidence interval is affected by this change?

The width of the new interval is about the same width as the original interval.
The width of the new interval is about twice the width of the original interval.
The width of the new interval is about one half the width of the original interval.
The width of the new interval is about one fourth the width of the original interval.
The width of the new interval is about four times the width of the original interval.

Question

2004ejo 2004ejo

01-04-2021
Mathematics

Answered

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A researcher has conducted a survey using a simple random sample of 50 licensed drivers to create a confidence interval to estimate the proportion of licensed drivers favoring the construction of a new stoplight. Assume that the sample proportion does not change. The researcher now decides to survey a random sample of 200 people instead of 50 licensed drivers. Which of the following statements best describes how the confidence interval is affected by this change?

The width of the new interval is about the same width as the original interval.
The width of the new interval is about twice the width of the original interval.
The width of the new interval is about one half the width of the original interval.
The width of the new interval is about one fourth the width of the original interval.
The width of the new interval is about four times the width of the original interval.

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