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 n=974 and x=551 who said "yes." Use a 90% confidence level?

A.Find the best point estimate of the population proportion P=

B.Identify the value of the margin of error E=

C. Construct the confidence interval. ___< P< __

Answer #1

Solution :

Given that,

**Point estimate** = sample proportion =
= x / n = 551 / 974 = 0.566

Z_{/2}
= 1.645

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

= 1.645 * (((0.566 * 0.434) / 974)

= 0.026

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.566 - 0.026 < p < 0.566 + 0.026

**0.540** < p < **0.592**

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