Question

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 ±3 percentage points. given specific sample data, which confidence interval is wider: the 99% 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 99% 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 99% confidence interval because it contains 100% - 80% = 20% of the true population parameters, while the 99% confidence interval only contains 100% - 99% = 1% of the true population parameters.

○ c. a 99% confidence interval must be wider than an 80% confidence interval because it contains 99% of the true population parameters, while the 80% confidence interval only contains 80% of the true population parameters.

○ d. a 99% 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.

Explanation:

The confidence level of a confidence interval indicates the probability that the interval will contain the true population parameter. A higher confidence level requires a wider interval. This is because to be more confident (e.g., 99% confident compared to 80% confident) that the interval captures the true value of the population proportion, the interval needs to be wider to account for more possible values.

Answer:

D. A 99% 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.