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 1013 and x equals 561 who said? "yes." Use a 90 % confidence level.

Answer 1

Solution :

Given that,

n = 1013

x = 561

= x / n = 561 /1013 = 0.554

1 - = 1 - 0.554 = 0.446

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.554 * 0.446 ) / 1013 ) = 0.026

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.554 - 0.026 < p < 0.554 + 0.026

0.528< p < 0.580

The 90% confidence interval for the population proportion p is : ( 0.528 , 0.580)