Question

To compare the average amount of time that canadians and americans spend commuting, a researcher collects a sample of canadians and americans. The canadians spend an average of hours a week commuting, with a standard deviation hours. The mean and standard deviation for the sample of americans is hours and hours, respectively. The standard error of the difference of sample means is:.

Answer 1

The standard error of the difference of sample means is 0.444

From the complete question, we have the following parameters

Canadians

• Sample size = 50
• Mean = 4.6
• Standard deviation = 2.9

Americans

• Sample size = 60
• Mean = 5.2
• Standard deviation = 1.3

The standard error of a sample is the quotient of the standard deviation and the square root of the sample size.

This is represented as:

$SE = \frac{\sigma}{\sqrt n}$

The standard error of the Canadian sample is:

$SE_1 = \frac{2.9}{\sqrt{50}}$

So, we have:

$SE_1 = 0.41$

The standard error of the American sample is:

$SE_2 = \frac{1.3}{\sqrt{60}}$

So, we have:

$SE_2 = 0.17$

The standard error of the difference of sample means is then calculated as:

$SE= \sqrt{SE_1^2 + SE_2^2}$

This gives

$SE= \sqrt{0.41^2 + 0.17^2}$

$SE= \sqrt{0.197}$

Take square roots

$SE= 0.444$

Hence, the standard error of the difference of sample means is 0.444

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