Question

A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1000and x=557 who said "yes". Use a 90%confidence level.

A) Find the best point estimate of the population P. (Round to three decimal places as needed)

B) Identify the value of margin of error E. ________ (Round to four decimal places as needed)

C) Construct a confidence interval. ___ < p <. (Round to three decimal places as needed)

D) Write a statement that correctly interprets the confidence interval. Choose the correct answer bellow

a) One has 99% conficence that the interval from the lower bound to the upper boundactually does contain the true value of the population proportion.

b) 99% of sample proportions will fall between the lower bound and the upper bound.

c) there is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

d) One has 99% confidence that the sample proportion is equal to the population proportion

Answer 1

Ans(A) For the given data of n=1000 people were asked if they feel vulnerable to identify theft our of which x=557 said yes. So the best point estimate of the population proportion is , which is called as the sample proportion.

(B) Margin of error will be calculated as follows:

(C) The formula to calculate the confidence interval is

Since it is given in the question that we need to calculate the 90% confidence interval.

Margin of error(ME)=0.0258, as calculated in part(B)

So the 90% confidence interval for the population proportion p is:

                   =0.557 0.0258

                   = (0.557-0.0258, 0.557+0.0258)

                   = 0.5312, 0.5828 0.531, 0.583

So, the 90% confidence interval for the population proportion is 0.531, 0.583. Or we can say that we are 90% confident that this interval contain the true value of population proportion, i.e., 0.531<p<0.583

(D). The correct option is (a), i.e., One is 99% confident that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.