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=905 and x=587 who said​ "yes." Use a 95% confidence level.

A. find the best point of estimate of the population of portion p.

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 = 905

x = 587

A) Point estimate = sample proportion = = x / n = 587 / 905 = 0.6486

1 - = 1 - 0.6486 = 0.3514

B) At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = Z 0.025 = 1.96

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

= 1.96 * (((0.6486 * 0.3514) / 905 )

= 0.0311

C) A 95% confidence interval for population proportion p is ,

- E < p < + E

0.6486 - 0.0311 < p < 0.6486 + 0.0311

0.618 < p < 0.680

D) With 95% confidence,that true proportion if they felt vulnerable to identity theft between 0.618 and 0.680.