A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago.A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken.You are given the following information. The standard error of - is
A) 12.9.
B) 9.3.
C) 4.
D) 2.

Question

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago.A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken.You are given the following information.  ​ The standard error of  -  is
A) 12.9. 
B) 9.3. 
C) 4. 
D) 2.

Quizplus · Accepted Answer

We are given the standard error of the difference between the two groups, which is the standard deviation of the sampling distribution of the difference between means. To find the standard error of the mean difference, we divide this standard deviation by the square root of the sample size. However, we are not given the sample sizes, so we cannot calculate the exact standard error of the mean difference. Therefore, we must use the approximation that the standard error of the mean difference is equal to the standard error of the difference divided by the square root of 2 (assuming equal sample sizes).

SE(mean diff) ≈ SE(diff) / sqrt(2)

According to the given information, the standard error of the difference is 4. Therefore,

SE(mean diff) ≈ 4 / sqrt(2) ≈ 2.83

So, the closest answer choice is D) 2.

A Statistics Teacher Wants to See If There Is Any