Question

a magazine provided results from a poll of 1500 adults who were asked to identify their favorite pie. among the 1500 respondents, 11% chose chocolate pie, and the margin of error was given as ±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?

a. 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.
b. 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.
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. 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.

Explanation:

Confidence interval width is related to the level of confidence. A higher confidence level means we want to be more sure that the interval contains the true population parameter. To be more confident (like 95% compared to 80%), the interval needs to be wider. For example, if we want to cover more possibilities (to be more confident), we have to expand the range.

Answer:

B. 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.