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=1000 and x equals x=559 who said​ "yes." Use a 95% confidence level.

Answer 1

Solution :

Given that,

n = 1000

x = 559

= x / n = 559 / 1000= 0.559

1 - = 1 - 0.559 = 0.441

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.559 * 0.441) / 1000) = 0.0308

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.559 - 0.0308 < p < 0.559 + 0.0308

0.5282 < p < 0.5898

The 95% confidence interval for the population proportion p is : ( 0.5282 , 0.5898)