Question

We are again studying the times required to solve two elementary math problems. Suppose we ask four students to attempt both Problem A and Problem B. Assume the students are independent and all results are normally distributed, but note that a particular student's times on the two questions are likely to be positively correlated. The results are presented below (in seconds).

student Problem A Problem B
1 20 35 2 30 40 2 3 15 20 4 40 50
Again find a two-sided 95% CI for the difference in the means of A and B.

Answer 1

(-16.494 ; -3.506)

Explanation:

student Prob A Prob B difference, d (A-B)

1 20 35____ - 15

2 30 40 ___ - 10

3 15 20 ___ - 5

4 40 50 __ - 10

Difference, d = -15, -10, -5, -10

Xd = Σd/ n = - 40 / 4 = - 10

Standard deviation of d ; Sd = 4.082

The confidence interval for the difference is given as :

Xd ± Tcritical*(Sd/√n)

Tcritical at 95%; df = n - 1 ; 4 - 1 = 3

Tcritical(0.05, 3)). = 3.182

C.I = -10 ± 3.182(4.082/√4)

C.I = -10 ± 6.494462

C. I = (-16.494 ; -3.506)