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