Question

in a poll of 520 human resource professionals, 45.8% said that body piercings and tattoos were big personal grooming red flags. complete parts (a) through (d) below.
238 (round to the nearest integer as needed)
b. construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big personal grooming red flags.
0.402 < p < 0.514
(round to three decimal places as needed.)
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?
a. the 80% confidence interval is wider than the 99% confidence interval. a confidence interval must be wider in order to be more confident that it captures the true value of the population proportion.
b. the 99% confidence interval is wider than the 80% confidence interval. a confidence interval must be wider in order to be less confident that it captures the true value of the population proportion.
c. the 80% confidence interval is wider than the 99% confidence interval. a confidence interval must be wider in order to be less confident that it captures the true value of the population proportion.
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.

Explanation:

• Confidence level and width of confidence interval: A higher confidence level requires a wider interval. This is because to be more confident that the interval captures the true population proportion, we need to allow for more possible values.
• Comparing 99% and 80% confidence intervals: The 99% confidence interval (0.402 < p < 0.514) is wider than the 80% confidence interval (0.430 < p < 0.486). As the confidence level increases from 80% to 99%, we need to be more sure that the interval contains the population proportion, so the interval widens.

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.