Question

Q1

A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll,

n=911 and

x=582 who said​ "yes." Use a

99% confidence level.

​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 three decimal places as​ needed.)

​c) Construct the confidence interval.

less than p less than

<p<

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

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

A.

99

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

B.

There is a

99

99​% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

C.

One has

99

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

D.

One has

99

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

Answer 1

a)

Number of Items of Interest,x =582

Sample Size,n = 911

Sample Proportion , p̂ = x/n = 0.639

best point estimate of the population proportion p = 0.639

b)

z -value =Zα/2 = 2.576                 [excel formula =NORMSINV(α/2)]

  

Standard Error , SE = √[p̂(1-p̂)/n] = 0.0159

margin of error , E = Z*SE = 2.576*0.0159=0.041

c)

99%Confidence Interval is

Interval Lower Limit = p̂ - E = 0.639-0.0410=0.5979

Interval Upper Limit = p̂ + E =0.639+0.0410=0.6799

  

99% confidence interval is (0.598< p < 0.680)

d)

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.