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 922 and x equals 557 who said​ "yes." Use a 99 % confidence level.

Answer 1

Solution :

Given that,

n = 922

x = 557

Point estimate = sample proportion = = x / n = 557/922=0.604

1 -   = 1- 0.604 =0.396

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* (((0.604*0.396) /922 )

E = 0.0415

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.604-0.0415 < p <0.604+ 0.0415

0.5625< p < 0.6455

The 99% confidence interval for the population proportion p is :lower limit= 0.5625,upper limit= 0.6455