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 1098 and x equals 564 who said​ "yes." Use a 90 % confidence level.

Answer 1

Solution :

Given that,

n = 1098

x = 564

= x / n = 564 /1098 = 0.514

1 - = 1 - 0.514 = 0.486

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.514 * 0.486) / 1098) = 0.025(rounded)

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.514 - 0.025 < p < 0.514+ 0.025

0.489 < p < 0.539