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 equals n=1087 and x equals x=553 who said​ "yes." Use a 90% confidence level.

Answer 1

Solution :

Given that,

n = 1087

x = 553

Point estimate = sample proportion = = x / n = 553/1087=0.509

1 -   = 1- 0.509 =0.491

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.509*0.491) / 1087)

E = 0.025

A 90% confidence interval proportion p is ,

- E < p < + E

0.509-0.025 < p < 0.509+0.025

0.484< p < 0.534

(0.484 , 0.534)