Question

Suppose the population of ages of all seven members of a tutoring service are: 22,17,19,21,20,19,24 A random sample of 3 members was taken and the ages were: 17,19,21. Determine the sampling error to 2 decimal places if this sample was used to estimate the population mean age.

Answer 1

6.36%

Explanation:

What we should do is calculate the mean value when we have all the data and then calculate the mean with the random samples, and calculate the error.

First, average of all data:

(22 + 17 + 19 + 21 + 20 + 19 + 24) / 7 = 20.29

Average for the random sample:

(17 + 19 + 21) / 3 = 19

% error = | sample - all / all | * 100

replacing the values:

% error = | (19 - 20.29) /20.29 | * 100

% error = 6.36%