Question

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

Answer 1

Answer:

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

Step-by-step 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:

$\sigma=\sqrt{\frac{\sigma_A^2}{n_A}+\frac{\sigma_B^2}{n_B}}$

Finally

$\sigma=\sqrt{\frac{17.6^2}{25}+\frac{21.2^2}{30}}\\\\\sigma= 5.23$