Question

A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n equals 1015 and x equals 565 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

c)Construct the confidence interval.
​(Round to three decimal places as​ needed.)

Answer 1

a) best point estimate of population proportion is p^ = X/n

p^ = 565/1015 = 0.557

b) for a = 0.05  

Z​​​​​​a/2 = Z​​​​​​0.025 = 1.96

Margin of error E = 1.96 * sqrt [0.557*0.443/1015]

E = 0.031

c) The 95% confidence interval for population proportion p

p^ - E < p < p^ + E

0.557 - 0.031 < p < 0.557 + 0.031

0.526 < p < 0.588