Question

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n=990 and x=558 who said​ "yes." Use a 99 % confidence level.

a) Find the best point estimate of the population proportion

0.564 ​(Round to three decimal places as​ needed.) ​

b) Identify the value of the margin of error E.

E = (Round to three decimal places as​ needed.)

Answer 1

Solution :

Given that,

n = 990

x = 558

(A)

Point estimate = sample proportion = = x / n = 558 / 990=0.564

1 -   = 1- 0.564 =0.436

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 )

(B)

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

= 2.576* (((0.564*0.436) / 990)

= 0.0405986

Margin of error = E = 0.041 rounded