Question

Two researchers select a sample for a population with a mean of 12.4 and a standard deviation of 9. Researcher A selects a sample of 30 participants. Researcher B selects a sample of 40 participants. Which sample is associated with a smaller standard error?
a. Researcher A's, because the sample size was smaller.
b. Researcher B's, because the sample size was smaller.
c. Researcher A's, because the sample size was larger.
d. Researcher B's, because the sample size was larger.

Answer 1

Answer: Option 'd' is correct.

Step-by-step explanation:

Since we have given that

Researcher A :

Mean = 12.4

Standard deviation = 9

sample size = 30

So, the standard error is given by

$\dfrac{\sigma}{\sqrt{n}}\\\\=\dfrac{9}{\sqrt{30}}\\\\=1.643$

Researcher B:

Mean = 12.4

Standard deviation = 9

Sample size = 40

So, the standard error is given by

$\dfrac{\sigma}{\sqrt{n}}\\\\=\dfrac{9}{\sqrt{40}}\\\\=1.423$

Sample B has smaller standard error than sample A because the sample size was larger than A.

Hence, Option 'd' is correct.