Question

An article included the following statement: "Few people believe there's much reality in reality TV: a total of 76% said the shows are either 'totally made up' or 'mostly distorted.'" This statement was based on a survey of 1006 randomly selected adults. Compute a bound on the error (based on 95% confidence) of estimation for the reported proportion of 0.76. (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

sample proportion, = 0.76
sample size, n = 1006
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.76 * (1 - 0.76)/1006) = 0.0135

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0135
ME = 0.026

Bound on error = 0.026

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 2.6% of the sample proportion of 76%.