Question

A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n equals 906 and x equals 529 who said​ "yes." Use a 90 % confidence level.

Answer 1

Solution:

Given,

n = 906 ....... Sample size

x =529 .......no. of successes in the sample

Let denotes the sample proportion.

     = x/n   = 529/906 = 0.5839

Our aim is to construct 90% confidence interval.

c = 0.9

= 1 - c = 1- 0.9 = 0.10

  /2 = 0.05 and 1- /2 = 0.95

Search the probability 0.95 in the Z table and see corresponding z value

= 1.645

Now , the margin of error is given by

E = /2 *  

= 1.645 * [0.5839 *(1 - 0.5839)/906]

= 0.0269

Now the confidence interval is given by

( - E)   ( + E)

(0.5839 - 0.0269)    (0.5839 + 0.0269)

0.557 0.611

i.e.

(0.557 , 0.611)

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