Question

Two researchers select samples of the same size. Researcher A selects a sample from a population with a standard deviation equal 10. Researcher B selects a sample from a population with a standard deviation equal 20. Which researcher selected a sample associated with a larger standard error?

Answer 1

Answer: Sample B

Step-by-step explanation:

The formula to calculate the standard error of a data is given by :-

`S.E.=(\sigma)/(√(n))`

Let n be the size of the both samples .

Given : Standard deviation of sample A
`\sigma_1=10`

Standard deviation of sample B
`\sigma_2=20`

From the formula it can be seen that the standard error is directly proportional to the standard error of the sample.

So if sample size for both the samples are same , then the a sample with greater standard deviation has the greater standard error .

Since , 20>10

Therefore, Sample B has associated with a larger standard error .