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 1056n=1056 and x equals 598x=598 who said​ "yes." Use a 90 % 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

a) Best point estimate = x/n = 598/1056 = 0.566

b) For 90% confidence, z = 1.645

Hence,

Margin of error

E = 0.025

c) Confidence interval:

(0.566 - 0.025, 0.566 + 0.025)

(0.541, 0.591)

d) We are 90% confident that the true proportion of respondents who felt vulnerable to identity theft will be between 54.1% and 59.1%.