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=1003 and x = 519 who said "yes." Use a 99% confidence level.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.)

Answer 1

Part a

p=x/n = 519/1003= 0.517

Part b

The margin of error is given by:

`ME=z_{(\alpha)/(2)}\cdot\sqrt[]{(p(1-p))/(n)}`

At 99 % confidence level the z value is z= 2.576

Replacing we got:

`ME=2.576\cdot\sqrt[]{(0.517(1-0.517))/(1003)}=0.0407`

Rounded it would 0.041

Part c

For this case we can find the confidence interval on this way:

`0.517\pm0.041=(0.476;0.558)`

Part d

For this case the correct answer is:

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