A particular subdivision has 20 homes.The number of people living in each of these homes is listed as follows: If a random sample of n = 3 homes were selected,what would be the highest possible positive sampling error?
A)6.0
B)3.0
C)0.5
D)2.5

Question

A particular subdivision has 20 homes.The number of people living in each of these homes is listed as follows:  If a random sample of n = 3 homes were selected,what would be the highest possible positive sampling error?
A)6.0 
B)3.0 
C)0.5 
D)2.5

Quizplus · Accepted Answer

To find the highest possible positive sampling error, we need to use the formula for the margin of error: 
Margin of error = critical value x standard error

Since the sample size is only 3, we have to use a t-distribution and the critical value for a 95% confidence interval with 2 degrees of freedom is 4.303.

The standard error can be calculated as the standard deviation of the population divided by the square root of the sample size. Using the given data, the standard deviation is approximately 3.297.

Therefore, the margin of error is 4.303 x 3.297 / √3 ≈ 2.462.

So the highest possible positive sampling error would be 2.5 (rounded up to the nearest half). The answer is D.

A Particular Subdivision Has 20 Homes