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.

Today Five Years Ago
x 82 88
σ2 112.5 54
n 45 36

The standard deviation of the difference between the means of the two populations is ______.

Answer 1

Answer:The standard deviation of the difference between the means of the two populations is 2.

Explanation:

The given table :

Today Five years ago

`\overline{x}=\ \ \ \ 82\ \ \ \ \ 88\\\sigma^2=\ \ 112.5\ \ 54\\n=\ \ \ \ 45\ \ \ \ \ 36`

Let A denotes the scores from students enrolled today and B denotes the scores from students enrolled five years ago.

Then, the standard deviation of the difference between the means of the two populations would be :-

`S.E._{\overline{x}_A-\overline{x}_B}}=\sqrt{(\sigma^2_A)/(n_1)+(\sigma^2_B)/(n_2)}\\\\=\sqrt{(112.5)/(45)+(54)/(36)}\\\\=√(4)=2`

Hence, the standard deviation of the difference between the means of the two populations is 2.