Use the sample data and confidence level given below to comp

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=985 and x=558 who said \"yes.\" Use a 90% 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 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 90% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

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

C.There is a 90% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

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

Solution

a.

Mean(x)=558
Sample Size(n)=985
Best point estimate = Sample proportion = x/n =0.566

b.
Margin of Error = Z a/2 Sqrt(p*(1-p)/n))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=558
Sample Size(n)=985
Sample proportion =0.566
Margin of Error = Z a/2 * ( Sqrt ( (0.566*0.434) /985) )
= 1.64* Sqrt(0)
=0.026

c.
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Confidence Interval = [ 0.566 ±Z a/2 ( Sqrt ( 0.566*0.434) /985)]
= [ 0.566 - 1.64* Sqrt(0) , 0.566 + 1.64* Sqrt(0) ]
= [ 0.54,0.592]
d.
C.There is a 90% chance that the true value of the population proportion will fall between the lower bound and the upper bound.