Final answer:
To construct a 99% confidence interval for the population proportion, the sample proportion is calculated by dividing the number of adults who have started paying bills online in the last year by the total sample size. The standard error is then calculated using the formula, and the confidence interval is constructed using the formula with the critical value. The confidence interval indicates the range within which we are 99% confident the true population proportion falls.
Step-by-step explanation:
To construct a confidence interval for the population proportion, we first need to calculate the point estimate, which is the sample proportion. In this case, the sample proportion is 1477/2859 = 0.516. Next, we need to calculate the standard error, which can be found using the formula:
SE = sqrt[(p_hat * (1 - p_hat)) / n]
where p_hat is the sample proportion and n is the sample size. The standard error is:
SE = sqrt[(0.516 * (1 - 0.516)) / 2859] ≈ 0.009
Finally, we can construct the confidence interval using the formula:
CI = p_hat ± (z * SE)
where z is the critical value corresponding to the desired confidence level. For a 99% confidence level, the z value is approximately 2.576. Substituting the values into the formula, we get:
CI = 0.516 ± (2.576 * 0.009)
Simplifying, the confidence interval is approximately:
CI = (0.492, 0.54)
This means that we are 99% confident that the true population proportion of adults who have started paying bills online in the last year falls within the range of 0.492 to 0.54.