Question

The researcher has limited resources. He sends 9 emails from a Latino name, and 14 emails from a non-Latino name. For the Latino names, the mean response time was 421 minutes (standard deviation of 82 minutes). For the non-Latino names, it was 366 minutes (standard deviation of 101 minutes). Calculate the standard error for the difference in means.

Answer 1

Answer: 38.41 minutes

Step-by-step explanation:

The standard error for the difference in means is given by :-

$SE.=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma^2_2}{n_2}}$

where , $\sigma_1$ = Standard deviation for sample 1.

$n_1$= Size of sample 1.

$\sigma_2$ = Standard deviation for sample 2.

$n_2$= Size of sample 2.

Let the sample of Latino name is first and non -Latino is second.

As per given , we have

$\sigma_1=82$

$n_1=9$

$\sigma_2=101$

$n_2=14$

The standard error for the difference in means will be :

$SE.=\sqrt{\dfrac{(82)^2}{9}+\dfrac{(101)^2}{14}}$

$SE.=\sqrt{\dfrac{6724}{9}+\dfrac{10201}{14}}$

$SE.=\sqrt{747.111111111+728.642857143}$

$SE.=\sqrt{1475.75396825}=38.4155433158\approx38.41$

Hence, the standard error for the difference in means =38.41 minutes