Question

A researcher selects two samples of 64 participants each. In the first sample, the population mean was 10 and the variance was 16. In the second sample, the population mean was 25 and the variance was 9. Which sample will be associated with a larger standard error of the mean

Answer 1

Answer:

Sample 1 is associated with a larger standard error of the mean.

Step-by-step explanation:

We are given the following in the question:

Formula for standard error:

$\text{Standard error} = \dfrac{\sigma}{\sqrt{n}}$

Sample 1:

$n = 64\\\mu = 10\\\sigma^2 = 16\\\sigma = \sqrt{16} = 4\\\\\text{Standard error} = \dfrac{4}{\sqrt{64}} = \dfrac{4}{8} = 0.5$

Sample 2:

$n = 64\\\mu = 25\\\sigma^2 = 9\\\sigma = \sqrt{9} = 3\\\\\text{Standard error} = \dfrac{3}{\sqrt{64}} = \dfrac{3}{8} = 0.375$

Thus, sample 1 is associated with a larger standard error of the mean.