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

Explanation:

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

`SE.=\sqrt{(\sigma_1^2)/(n_1)+(\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{((82)^2)/(9)+((101)^2)/(14)}`

`SE.=\sqrt{(6724)/(9)+(10201)/(14)}`

`SE.=√(747.111111111+728.642857143)`

`SE.=√(1475.75396825)=38.4155433158\approx38.41`

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