Question

Which relationship between sample size and sampling error is correct? Question 36 options:

a) The smaller the sample, the smaller the sampling error will be.
b) The larger the sample, the smaller the sampling error will be.
c) Sampling error and poll size are unrelated.
d) The wording of poll questions will determine sampling error.

Answer 1

Answer: option B

Explanation: The sampling error also known as the marginal error is given mathematically as

Margin of error = critical value × (standard deviation/√n)

Where n = sample size

As we can see from this formulae, the only variable here is the margin of error and the sample size.

Hence margin of error = k/√n

Which implies that there is an inverse relationship between margin of error and sample size.

A large sample size gives a low margin of error while a small sample size gives a large margin of error.

Answer 2

The relationship between the size of the sample and the sample error should be that the more the sample the small should be the sample error.

Relationship between the sample size and sampling error:

We know that

Margin of error = critical value × (standard deviation/√n)

Here n = sample size

Also,

Margin of error = k/√n

This shows that there should be an opposite relation between the margin of error and the size of sample.

Hence, the option b is correct.

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