Question

To compare the average amount of time that Canadians and Americans spend commuting, a researcher collects a sample of 50 Canadians and 60 Americans. The Canadians spend an average of 4.6 hours a week commuting, with a standard deviation 2.9 hours. The mean and standard deviation for the sample of Americans is 5.2 hours and 1.3 hours, respectively. The standard error of the difference of sample means is:

Answer 1

Using it's formula, it is found that the standard error of the difference of sample means is of 0.443.

The standard error for each sample is given by the sample standard deviation divided by the square root of the sample size, hence:

$s_C = \frac{2.9}{\sqrt{50}} = 0.41$

$s_A = \frac{1.3}{\sqrt{60}} = 0.168$

For the distribution of the difference of sample means, the standard error is the square root of the sum of the standard error of each sample squared, hence:

$s = \sqrt{s_C^2 + s_A^2} = \sqrt{0.41^2 + 0.168^2} = 0.443$

The standard error of the difference of sample means is of 0.443.

You can learn more about the standard error of the difference of sample means at https://brainly.com/question/25959526