Question

In a simple random sample of 1600 people age 20 and over in a certain​ country, the proportion with a certain disease was found to be 0.130 ​(or 13.0​%). complete parts​ (a) through​ (d) below.

what is the standard error of the estimate of the proportion of all people in the country age 20 and over with the​ disease?

Answer 1

The standard error of the estimate of the proportion of all people in the country age 20 and over with the disease is approximately 0.0084 or 0.84%, calculated using the formula for the standard error of a sample proportion.

Step-by-step explanation:

The standard error of the proportion in a sample is calculated using the formula for the standard error of a sample proportion, which is the square root of (p(1-p)/n), where p is the sample proportion and n is the sample size.

Step 1: Identify the sample proportion (p) and sample size (n)

1. Sample proportion (p) = 0.130 or 13%
2. Sample size (n) = 1600

Step 2: Calculate the standard error of the proportion

Using the formula:

Standard error (SE) = √(p(1-p)/n)

SE = √(0.130(1-0.130)/1600)

SE = √(0.130*0.870/1600)

SE = √(0.1131/1600)

SE = √(0.0000706875)

SE ≈ 0.0084

Therefore, the standard error of the estimate of the proportion of all people in the country age 20 and over with the disease is approximately 0.0084 or 0.84%.