Question

In a poll of 525 human rescourse professionals, 49.5% said that body piercings and tattoos were big red flags. Complete parts a through d below.

A. Among the 525 how many of them said it’s a red flag

B. Construct a 99% confidence interval estimate of the proportion of all professionals believing that it’s a red flag

C. Repeat part B with a 80% confidence level

D. Is B or C a wider interval and why?

Answer 1

Given,

proportion = 0.495 . n = 525

A)

Among 525, number of the said it's a red flag = 525 * 0.495

= 259.875 ( 260 Rounded to nearest integer)

B)

99% confidence interval for proportion p is

- Z/2 * sqrt( ( 1 - ) / n) < p < + Z/2 * sqrt( ( 1 - ​) / n)

0.495 - 2.5758 * sqrt( 0.495 * 0.505 / 525) < p < 0.495 + 2.5758 * sqrt( 0.495 * 0.505 / 525)

0.439 < p < 0.551

99% CI is ( 0.439 , 0.551)

c)

80% confidence interval for p is

- Z/2 * sqrt( ( 1 - ) / n) < p < + Z/2 * sqrt( ( 1 - ​) / n)

0.495 - 1.2816 * sqrt( 0.495 * 0.505 / 525) < p < 0.495 + 1.2816 * sqrt( 0.495 * 0.505 / 525)

0.467 < p < 0.523

80% CI is ( 0.467 , 0.523 )

d)

Confidence level of 99% have wider interval than 80% confidence level.

Because nterval width for 99% level increases for higher accuracy of confidence level,

that is true value of proportion is more likely to be within the confidence interval.