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=1037 and x=509 who said​ "yes." Use a 99% confidence level.

Click the icon to view a table of z scores.

​a) Find the best point estimate of the population proportion p.

​(Round to three decimal places as​ needed.)

​b) Identify the value of the margin of error E.

E=

​(Round to three decimal places as​ needed.)

​c) Construct the confidence interval.

p <p<

​(Round to three decimal places as​ needed.)

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

A.

There is a 9999​% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

B.

One has 9999​% confidence that the sample proportion is equal to the population proportion.

C.

One has 9999​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

D.

9999​% of sample proportions will fall between the lower bound and the upper bound.

Answer 1

Given that, n = 1037 and x = 509

a) sample proportion is,

h

Te best point estimate of the population proportion p is 0.491

b) A 99% confidence level has significance level of 0.01 and critical value is,

Margin of error (E) is,

=> E = 0.040

c) 99% confidence interval for p is,

0.491 - 0.040 < p < 0.491 + 0.040

0.451 < p < 0.531

d) Interpretation is,

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.