Question

A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n=946 and 1x=591 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.

d)Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

Answer 1

Solution :

n =946

x = 591

= x / n = 591/ 946 = 0.625

1 - = 1 - 0.625 = 0.735

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 = 1.960

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

= 1.960* (((0.625 * 0.375) / 946)

= 0.031

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.625 - 0.031 < p < 0.625 + 0.031

0.594 < p < 0.656