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 931n=931

and

x equals 596x=596

who said​ "yes." Use a

99 %99%

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.

. 552.552

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

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

Eequals=. 511.511

​(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.

One has

9999​%

confidence that the sample proportion is equal to the population proportion.

B.

9999​%

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

C.

One has

9999​%

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

9999​%

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

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Answer 1

Given that x=596 n=931

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

p = x / n = 596/ 931= 0.640

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

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.990 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.58

Margin of error = E = Z _{/ 2} * ((P * (1 - P)) / n)

= 2.58 * (((0.640 * 0.360) / 931) = 0.020

#Margin of error=0.020

c) Construct the confidence interval.

A 99 % confidence interval for population proportion p is ,

P - E < P <P + E

0.640 - 0.020 < p < 0.640+ 0.020

0.620 < p < 0.660

d)correctly interprets the confidence interva

c) 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.