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=1007 and x=571 who said yes. Use a 95% confidecne level.

A. find the best point of estimate of the population of portion p. (Round to three decimal places as​ needed.)

B. Identify the value of the margin of error E. E= round to four decimal places as needed.

C. Construct the confidence interval. _ < p <_ round to three decimal places.

D. Write a statement that correctly interprets the confidence interval.

Answer 1

Solution :  

Given that,

n = 1007

x = 571

A.

Point estimate = sample proportion = = x / n = 571 / 1007 = 0.567

1 - = 1 - 0.567 = 0.433

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

B.

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

= 1.96 * (((0.567 * 0.433) / 1007)

= 0.0306

C.

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.567 - 0.0306 < p < 0.567 + 0.0306

0.536 < p < 0.598

The 95% confidence interval for the population proportion p is : 0.536 , 0.598

D.

Statement The 95'' confidence interval is Ts