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 1006 and x equals 554 who said​ "yes." Use a 99 % 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.

A. 99​% of sample proportions will fall between the lower bound and the upper bound.

B. One has 99​% confidence that the sample proportion is equal to the population proportion.

C. One has 99​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

D. There is a 99​% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

Answer 1

a)

0.551

b)

MOE = z_α/2•√p̂(1 - p̂)/n = 0.016

c)

CI

z_α/2 = 2.5758293064

Lower Bound = p̂ - z_α/2•√p̂(1 - p̂)/n = 0.551 - (2.5758293064)(0.015681946921365753) = 0.5106059815

Upper Bound = p̂ + z_α/2•√p̂(1 - p̂)/n = 0.551 + (2.5758293064)(0.015681946921365753) = 0.5913940185

Confidence Interval = (0.511, 0.591)

d)

C. One has 99​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.