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 results. T
oday 5 Years Ago Mean 82 88 Variance 112.5 54 Sample Size 45 36
The standard deviation of the difference between the means of the two populations is
A) 12.9
B) 9.3
C) 4
D) 2

Answer 1

Answer: D) 2

Step-by-step explanation:

The standard deviation of the difference between the means of the two populations is given by:-

$S.E.=\sqrt{\dfrac{\sigma^2_1}{n_1}+\dfrac{\sigma^2_2}{n_2}}}$

where $n_1$= sample size of population 1

$n_2$= sample size of population 2

$\sigma^2_1$= variance of population 1

$\sigma^2_2$= variance of population 2

As per given,

$S.E.=\sqrt{\dfrac{112.5}{45}+\dfrac{54}{36}}}\\\\=\sqrt{4}\\=2$

Hence, the correct option is D) 2.