Question

In a Harris poll of 514 human resource professionals, 90% said that the appearance of a job applicant is most important for a good first impression. Construct a 99% confidence interval for the proportion of all human resource professionals believing that the appearance of a job applicant is most important for a good first impression. Also, find the margin of error.

Answer 1

Solution :

Given that,

n = 514

Point estimate = sample proportion = =90%=0.90

1 -   = 1- 0.90 =0.10

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

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

= 2.576* (((0.90*0.10) /514 )

E = 0.034

A 99% confidence interva proportion p is ,

- E < p < + E

0.90 - 0.034 < p < 0.90+0.034

0.866< p < 0.934

(0.866 , 0.934 )