Question

In a simple random sample of 800 people aged 20 and over in a certain country, the proportion with a certain disease was found to be 0.115 (or 11.5%).

(a) What is the standard error of the estimate of the proportion of all people in the country aged 20 and over with the disease?

Answer 1

The standard error of the estimate of the proportion can be calculated using the formula sqrt((p * (1 - p)) / n), where p is the proportion with the disease and n is the sample size. Substituting the given values, we find that the standard error is approximately 0.011.

Step-by-step explanation:

The standard error of the estimate of the proportion of all people in the country aged 20 and over with the disease can be calculated using the formula:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the proportion with the disease and n is the sample size.

Substituting the given values, we have:

Standard Error = sqrt((0.115 * (1 - 0.115)) / 800)

Standard Error = sqrt((0.115 * 0.885) / 800)

Standard Error ≈ 0.011 (rounded to three decimal places)

Therefore, the standard error of the estimate of the proportion of all people in the country aged 20 and over with the disease is approximately 0.011.