Practise interpreting confidence intervals for population proportions, explaining confidence through repeated sampling, and using estimates with margins of error.
In a random sample of 500 American adults, 210 expressed the belief that journalists have "low" ethical standards. A 95\% confidence interval for the proportion of all American adults who believe that journalists have "low" ethical standards is given by (0.3767, 0.4633). Which of the following is a correct interpretation of the confidence level of 95\%?
There is a 0.95 probability that the true proportion of all American adults who believe that journalists have "low" ethical standards is between 0.3767 and 0.4633.
We are 95\% confident that the true proportion of all American adults who believe that journalists have "low" ethical standards is between 0.3767 and 0.4633 .
If the proportion of American adults who believe that journalists have "low" ethical standards is calculated for repeated random samples of 500 adults, 95\% of these sample proportions will fall between 0.3767 and 0.4633 .
If a confidence interval for the proportion of American adults who believe that journalists have "low" ethical standards is calculated for repeated random samples of 500 American adults, approximately 95\% of these intervals will contain the true population proportion.
D