Question

An article included the following statement: "Few people believe there's much reality in reality TV: a total of 82% said the shows are either 'totally made up' or 'mostly distorted.'" This statement was based on a survey of 1004 randomly selected adults. Compute a bound on the error (based on 95% confidence) of estimation for the reported proportion of 0.82. (Round your answer to three decimal places.)

Interpret the bound. (Round your answers to one decimal place.) We are _________% confident that the proportion of all adults who believe that the shows are either "totally made up" or "mostly distorted" is within _______ % of the sample proportion of ________%.

Answer 1

Given that,

= 0.82

1 - = 1 - 0.82= 0.18

n = 1004

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

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

= 1.96 * (((0.82* 0.18) / 1004) = 0.024

interpret the bound. (Round your answers to one decimal place.) We are 95 % confident that the proportion of all adults who believe that the shows are either "totally made up" or "mostly distorted" is within 0.024  % of the sample proportion of 82%.