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 1089 and x equals 572 who said​ "yes." Use a 95 % confidence level. a) Find the best point estimate of the population proportion p. b) Identify the value of the margin of error E. E= c) Construct the confidence interval. _

Answer 1

Solution :

Given that,

n = 1089

x = 572

a) Point estimate = sample proportion = = x / n = 572 / 1089 = 0.525

1 - = 1 - 0.525 = 0.475

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.960 (((0.525 * 0.475) / 1089 )

= 0.030

c) A 95% confidence interval for population proportion p is ,

± E  

0.525 ± 0.030

(0.495 , 0.555)