Question

a magazine provided results from a poll of 200 adults who were asked to identify their favorite pie. among the 200 respondents, 12% chose chocolate pie, and the margin of error was given as ±3 percentage points. given specific sample data, which confidence interval is wider: the 90% confidence interval or the 80% confidence interval? why is it wider?
choose the correct answer below.
a. 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.
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 80% 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 because it contains 90% of the true population parameters, while the 80% confidence interval only contains 80% of the true population parameters.
d. 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.

Explanation:

A higher confidence level requires a wider interval. A 90% confidence interval is more confident (has a higher probability) of capturing the true population proportion than an 80% confidence interval. To be more confident, the interval needs to be wider.

Answer:

A. 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.