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=1098 and x equals x=537 who said​ "yes." Use a 99% confidence level.

Answer 1

Solution :

Given that,

n = 1098

x = 537

Point estimate = sample proportion = = x / n = 537/1098=0.489

1 - = 0.511

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )   

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

= 1.96 (((0.489*0.511) / 1098)

= 0.030

A 95% confidence interval is ,

- E < p < + E

0.489 - 0.030 < p < 0.489 + 0.030

0.459  < p < 0.519

(0.459 , 0.519)