Question

A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1023 and x=546 who said "yes". Use a 99% confidence level.

A) Find the best point estimate of the population P. (Round to three decimal places as needed)

B) Identify the value of margin of error E. ________ (Round to four decimal places as needed)

C) Construct a confidence interval. ___ < p <. (Round to three decimal places as needed)

D) Write a statement that correctly interprets the confidence interval. Choose the correct answer below

Answer 1

Solution :

Given that,

n = 1023

x = 546

A) Point estimate = sample proportion = = x / n = 546 / 1023 = 0.534

1 - = 1 - 0.534 = 0.466

B) At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.576

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

= 2.576 (((0.534 * 0.466) / 1023)

= 0.0402

C) A 99% confidence interval for population proportion p is ,

- E < p < + E

0.534 - 0.0402 < p < 0.534 + 0.0402

(0.494 < p < 0.574 )

D) We are 99% confident that the true proportion if they felt vulnerable to identity theft is between 0.494 and 0.574.