Answer:
To calculate the standard error (SE), margin of error, and the 95% confidence interval for the proportion of people in the country age 20 and over with the disease, we can use the following formulas:
a. Standard Error (SE) of the estimate:
SE = sqrt[(p * (1 - p)) / n]
where p is the proportion with the disease and n is the sample size.
SE = sqrt[(0.145 * (1 - 0.145)) / 1000]
SE ≈ 0.0109 (rounded to four decimal places)
b. Margin of Error (ME):
ME = z * SE
where z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.
ME = 1.96 * 0.0109
ME ≈ 0.0214 (rounded to three decimal places)
c. Confidence Interval (CI):
CI = p ± ME
CI = 0.145 ± 0.0214
CI ≈ (0.123, 0.167) (rounded to three decimal places)
The 95% confidence interval for the proportion of people in the country age 20 and over with the disease is approximately (0.123, 0.167).
d. To determine if the confidence interval supports or refutes the claim that 15.6% of all people in the country age 20 or over have the disease, we can check if the value of 15.6% falls within the confidence interval.
Since the value 15.6% is not contained within the confidence interval (0.123, 0.167), we can conclude that the confidence interval does not support the claim.
