Question

In a poll of 568 human resource​ professionals, 35.9​% said that body piercings and tattoos were big grooming red flags. Complete parts​ (a) through​ (d) below. ​a) Among the 568 human resource professionals who were​ surveyed, how many of them said that body piercings and tattoos were big grooming red​ flags? 204 ​(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 grooming red flags. . 307less than p less than 0.411 ​(Round to three decimal places as​ needed.) ​c) Repeat part​ (b) using a confidence level of​ 80%. nothingless than p less than nothing ​(Round to three decimal places as​ needed.)

Answer 1

Solution :

Given that,

n = 568

Point estimate = sample proportion = = 0.359

1 - = 1 - 0.359 = 0.641

c) At 80% confidence level

= 1 - 80%

=1 - 0.80 =0.20

/2 = 0.10

Z/2 = Z_0.10 = 1.282

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.282 (((0.359 * 0.641) / 568 )

= 0.026

A 80% confidence interval for population proportion p is ,

- E < p < + E

0.359 - 0.026 < p < 0.359 + 0.026

( 0.333 < p < 0.385 )