Ross Howell

10/14/2023 · Primary School

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, \( 14 \% \) chose chocolate pie, and the margin of error was given as \( \pm 3 \) percentage points. Given specific sample data, which confidence interval is wider: the \( 95 \% \) confidence interval or the \( 80 \% \) confidence interval? Why is it wider? Choose the correct answer below. A. An \( 80 \% \) confidence interval must be wider than a \( 95 \% \) 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 \( 95 \% \) confidence interval because it contains \( 100 \%-80 \%=20 \% \) of the true population parameters, while the \( 95 \% \) confidence interval only contains \( 100 \%-95 \%=5 \% \) of the true population parameters. C. A \( 95 \% \) confidence interval must be wider than an \( 80 \% \) confidence interval because it contains \( 95 \% \) of the true population parameters, while the \( 80 \% \) confidence interval only contains \( 80 \% \) of the true population parameters. D. A \( 95 \% \) 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.