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=989 and x=599 who said "yes." Use a 90% 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 <___

(Round to three decimal places as needed.)

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

A. 90% of sample proportions will fall between the lower bound and the upper bound.

B. One has 90% confidence that the sample proportion is equal to the population proportion.

C. One has 90% 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 90% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

Answer 1

n=989 and x=599

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

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

Critical value of Z at 90% CI =1.645

E=0.606 +/- (1.645*0.015)

E=0.606 +/- 0.025

c) Construct the confidence interval.   

Lower limit=0.606-0.025=0.581

Upper limit =0.606+0.025=0.631

0.581<P<0.631

d)

One has 90% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion