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=1017

and

x=510

who said​ "yes." Use a99%

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.

​(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.

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

Answer 1

Solution :

n = 1017

x = 510

a ) = x / n =510 / 1017 = 0.501

1 - = 1 - 0.501= 0.499

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576* (((0.501 * 0.499) / 1017)

= 0.040

c ) A 99 % confidence interval for population proportion p is ,

- E < P < + E

0.501 - 0.040 < p < 0.501+ 0.040

0.461 < p < 0.541