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A magazine provided results from a poll of 1000 adults who were asked to identify their...

A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the1000 respondents, 13% chose chocolate pie, and the margin of error was given as ±5 percentage points. Given specific sample data, which confidence interval is wider: the 90% confidence interval or the 80% confidence interval? Why is it wider?

Group of answer choices

A. An 80​% confidence interval must be wider than a 90​% confidence interval in order to be more confident that it captures the true value of the population proportion.

B. An 80​% confidence interval must be wider than a 90​% confidence interval because it contains ​100% - 80​% = 20​% of the true population​ parameters, while the 90​% confidence interval only contains ​100% - 90​% = 10​% of the true population parameters.

C. A 90​% confidence interval must be wider than an 80​% confidence interval in order to be more confident that it captures the true value of the population proportion.

D. A 90​% confidence interval must be wider than an 80​% confidence interval because it contains 90​% of the true population​ parameters, while the 80​% confidence interval only contains 80​% of the true population parameters.

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Answer #1

Answer:

option C is correct

the length of confidence interval 90% = 2t0.95 sqrt of (p^(1-p^) / n

the length of confidence interval of 80% = 2t0.9 sqrt of (p^(1- p^)/n

so that t0.95 > t0.9

90% confidence interval is more wider and more confident it captures to be true value of population proportion

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