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A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll,...

A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n = 990 and x = 538 who said​ "yes." Use a 95 % confidence level.

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Expert Solution

Solution :

Given that,

n = 990

x = 538

Point estimate = sample proportion = = x / n = 538/990=0.543

1 -   = 1-0.543 =0.457

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2   * ((( * (1 - )) / n)

= 1.96 (((0.543*0.457) /990 )

E = 0.031

A 95% confidence interval is ,

- E < p < + E

0.543 - 0.031 < p < 0.543+0.031

0.512< p < 0.574

(0.512 , 0.574)

orchestra answered 1 year ago
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