Use the sample data and confidence level given below to complete parts (a) throu

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=914 and x=597 who said "yes." Use a 95% confidence level.

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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.(Round to four decimal places as needed.)

c) Construct the confidence interval.

? <p< ? (Round to three decimal places as needed.)

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

A.One has 95% confidence that the sample proportion is equal to the population proportion.

B.There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

C. 95% of sample proportions will fall between the lower bound and the upper bound.

D. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

Explanation / Answer

Solution:- Given that information: n = 914, x = 597

a) the best point estimate of the population proportion p =

p = 597/914 = 0.653
b) Margin of error = Z*sqrt(pq/n)

95% confidence interval for Z = 1.96
q = 1-p = 1 - 0.653 = 0.347
ME = 1.96*sqrt(0.653*0.347/914) = 0.0309
  
c) The confidence interval = P +/- ME
= 0.653 +/- 0.0309
= (0.6221 , 0.6839)
= (0.622 < p < 0.684)

d) option D. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

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