SAT HIGH SCHOOL

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:.

Answers

Answer 1

Answer:

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:

$SE = (\sigma)/(\sqrt n)$

The standard error of the Canadian sample is:

$SE_1 = (2.9)/(√(50))$

So, we have:

$SE_1 = 0.41$

The standard error of the American sample is:

$SE_2 = (1.3)/(√(60))$

So, we have:

$SE_2 = 0.17$

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

$SE= √(SE_1^2 + SE_2^2)$

This gives

$SE= √(0.41^2 + 0.17^2)$

$SE= √(0.197)$

Take square roots

$SE= 0.444$

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

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Answers

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