Question

You want to estimate the average difference between grades on a certain math exam before students take the associated math class and after they take the associated math class. (hopefully you do better after taking the class, right?) you take a random sample of 5 students and get the following results.

Grade before

54

25

73

23

42

Grade after

82

76

98

43

38

question before if that helps answer the question above : you want to estimate the difference between the average grades on a certain math exam before students take the associated math class. (Hopefully you do better after taking the class right?) You take random samples of 5 students who have taken the class and 5 students who have not taken the class. You get the following results (grades).

Not Taken

54

25

73

23

42

taken

82

76

98

43

38

Answer 1

Suppose, random variable X denotes grades before the math class whereas random variable Y denotes grades after the math class. Further we define random variable D as difference (D=Y-X) in grades after and before that math class.

Serial number (i)	Xi	Yi	Di=Yi-Xi
1	54	82	28
2	25	76	51
3	73	98	25
4	23	43	20
5	42	38	-4

Expected number of difference between grades is given by

So, estimated average difference is 24. It implies that on average every student's grade after the class is expected to increase by 24 from grade before the class.