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 equals n=963

and

x=587

who said​ "yes." Use a

90%

confidence level.

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Click the icon to view a table of z scores.

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

nothing

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

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

equals=nothing

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

​c) Construct the confidence interval.

nothing less than p less than<p<nothing

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

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

A.There is a

90%

chance that the true value of the population proportion 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.

90​%

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

Answer 1

The statistical software output for this problem is:

From above output:

a) Point estimate = 0.610

b) Margin of error = (0.6354 - 0.5840)/2 = 0.026

c) Confidence interval:

0.584 < p < 0.635

d) Option C is correct.