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 25 participants. Researcher B selects a sample of 15 participants. Which sample is associated with a larger standard error

Answer 1

researcher B with 15 participants will be associated with a larger standard error

Explanation:

Standard error can be expressed mathematically as;

E = zr/√n ......1

Where

z = z value of test statistics

r = standard deviation

n = number of samples

From equation 1, given that the standard deviation and the z value for the two researchers are thesame, then we can say;

E = zr/√n

E = k/√n

E1/E2 = √(n2/n1)

n1 = 25

n2 = 15

E1/E2 = √(15/25)

E1/E2 = 0.774596669241

E1 = 0.77E2

Therefore, E1 is less than E2

E1 < E2

And also the larger the number of samples the lower the standard error.

Since researcher B have a lower number of samples it will have a larger standard error.

So, researcher B with 15 participants will be associated with a larger standard error