Question

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=952 and x= 512 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.There is a 99​% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

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

Answer 1

Solution :

Given that,

n = 952

x = 512

(a)

Point estimate = sample proportion = = x / n = 512 / 952 = 0.538

1 - = 1 - 0.538 = 0.462

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

(b)

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

= 2.576 * (((0.538 * 0.462) / 952)

= 0.042

(c)

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.538 - 0.042 < p < 0.538 + 0.042

0.496 < p < 0.580

(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.