Question

c. repeat part (b) using a confidence level of 80%.
0.430 < p < 0.486
(round to three decimal places as needed.)
d. compare the confidence intervals from parts (b) and (c) and identify the interval that is wider. why is it wider?
o a. the 80% confidence interval is wider. a confidence interval must be wider in order to be more confident that it captures the
o b. the 80% confidence interval is wider. a confidence interval must be wider in order to be less confident that it captures the
o c. the 99% confidence interval is wider. a confidence interval must be wider in order to be less confident that it captures the
o d. the 99% confidence interval is wider. a confidence interval must be wider in order to be more confident that it captures the
true value of the population proportion.
true value of the population proportion.
true value of the population proportion.
true value of the population proportion.

Explanation:

Step1: Understand confidence interval width

A higher confidence level requires a wider interval. This is because to be more confident that the interval contains the true population proportion, we need to cover a larger range of values.

Step2: Compare 80% and 99% confidence levels

Since 99% confidence level is higher than 80% confidence level. A 99% confidence interval must be wider in order to be more confident that it captures the true value of the population proportion.

Answer:

D. The 99% confidence interval is wider than the 80% confidence interval. A confidence interval must be wider in order to be more confident that it captures the true value of the population proportion.