Question

The standard deviation of a sample taken from population A is 17.6 for a sample of 25.

The standard deviation of a sample taken from population B is 21.2 for a sample of 30.
The standard deviation of the sample mean differences is _____. Round your answer to the nearest hundredth.

Answer 1

5.23

Explanation:

Answer 2

The standard deviation of the sample mean differences is _5.23_

Explanation:

We have a sample of a population A and a sample of a population B.

For the sample of population A, the standard deviation
`\sigma_A` is

`\sigma_A = 17.6`

The sample size
`n_A` is:

`n_A = 25`.

For the sample of population B, the standard deviation
`\sigma_B` is

`\sigma_B = 21.2`

The sample size
`n_B` is:

`n_B = 30`.

Then the standard deviation for the difference of means has the following form:

`\sigma=\sqrt{(\sigma_A^2)/(n_A)+(\sigma_B^2)/(n_B)}`

Finally

`\sigma=\sqrt{(17.6^2)/(25)+(21.2^2)/(30)}\\\\\sigma= 5.23`